First, your radio is a Futaba 9C. It will work either as a PCM radio, or an FM (PPM) radio, selectable by YOU through a menu screen.
The receiver you have, an R148DF will work in the Trex, but it's kind of big and heavy. I'd recommend the smaller Futaba R146iP. It's PCM instead of FM/PPM, small, and very popular for Futaba radio owners who fly the Trex.
You DON'T use the radio's receiver battery pack to power your receiver, servos, and gyro. The Electronic Speed Control (ESC) generally has a built-in regulator that allows you to power your on-board radio equipment using the battery you will use to power the motor. The speed control plugs into the THROTTLE channel of your receiver, provides all radio power through that connection, and allows the transmitter to control the motor speed.
The LiPos you're looking at should be something on the order of Thunder Power Extreme 2070 mah, 3S1P battery (11.1 volts nominal), three single LiPo cells wired in series. There are a lot of different suitable batteries out there now, look for something that has a 20C or greater continuous discharge capacity to provide suitable performance.
The gyro that was recommended was a Futaba GY401, a very good gyro, but you need to learn how to properly install and set it up.
The tail rotor servo that was probably referred to you was a Futaba S9650. A very popular, small, digital servo. A good choice.
HItec HS65HB of HS65MG are great servos, you can't go wrong with them.
Your SE uses CCPM swashplate control, you'll have to enable 120 degree swash control in the swash menu of your transmitter for it to work. That would be swashplate SR-3 type in your TX.
The three swashplate servos would plug into the receiver channels labeled Aileron (channel 1), Elevator (channel 2), and AUX 1 (channel 6). The speed control plugs into channel 3 (throttle), gyro into channel 4 (rudder), the gyro gain control plugs into channel 5. You'll need to figure out how you want to control the gyro gain -- using either the channel 5 landing gear switch, or enable the gyro sense stuff in the TX, and set it up correctly.
That's your basic connector plug-in tutorial.
When setting up the flight controls, unplug the speed control from the receiver. Plug your normal nicad RX battery pack into the receiver so you can power the radio, gyro, and servos, without having to worry about the motor spinning up and scaring the bejeebers out of you (or worse).
Generic CCPM setup:
Enable the 120 degree, 3 servo CCPM feature in the transmitter before you do anything else. (Swash type SR-3 in your Futaba TX).
Once you enable the CCPM feature, you should then be able to select 120 degree CCPM mixing, and the SWASH AFR menu should be available to set the mix percentages for elevator, aileron, and pitch.
The three servos will plug into channels 1, 2, and 6 of your receiver.
Channel 1 is Aileron
Channel 2 is Elevator
Channel 6 is Auxiliary 1, and also happens to be the collective pitch servo channel.
Plug your servos into the correct channel on the RX. You have three servos controlling the swashplate. One servo connects to a ball that is either on the front or the rear of the swash and on the heli's centerline. The servo controlling this ball plugs into the ELEVATOR channel of your RX (channel 2).
The remaining two servos connect to the remaining two balls on the swash which aree 120 degrees apart. One will be on the left side of the heli, the other on the right side. These connect to the aileron (channel 1) and pitch (channel 6) plug. It doesn't matter which servo plugs into which channel, as long as one goes to 1, the other goes to 6.
Set all trim settings to zero, no trim in any direction.
Go to the SWASH AFR mix menu, and set ELEVATOR, AILERON, and PITCH numbers to +65.
This is only a starting point, we'll fix the SIGN of the number (+/-), and the SIZE of the number (bigger/smaller) later on down the page.
Ignore the direction of the servos for now. We're about to fix that:
Two servos in CCPM mix tilt the swash left and right. This is the aileron function. The third servo doesn't move at all when you move the stick side to side.
For elevator (fore/aft) control, all three servos tilt the swashplate fore and aft.
For collective pitch, all three servos move the swash up and down.
Go to your servo reversing menu in the TX.
Move the aileron stick to the right. The servos plugged into channels 2 and 6 must move in the opposite direction -- one must move UP, the other must move down. If they both move up, or both move down, reverse the direction of ONE of them (channel 1, or channel 6) at the transmitter channel reverse menu.
Don't worry if they don't seem to move the swash in the correct direction at this point, just make sure that they go in opposite directions when you move the stick left and right. You only need to reverse one servo (either channel 1 or channel 6), as the point here is just to get one to go up, one to go down at the same time.
Now, move the stick for fore/aft cyclic. The servo connected to the elevator channel (channel 2) on the RX needs to have its direction set so that when the pitch and aileron servo move UP together, the elevator servo moves down (and when the elevator servo moves up, the other two move down). Use the elevator reversing function (Channel 2) to make this happen. Don't touch the reversing for either channel 1 or 6.
At this point, the swash will tilt left and right when you move the aileron stick, it will tilt fore and aft when you move the elevator stick, and it will move up and down (level) when you move the collective stick.
The swash directions may be reversed at this point, but at least the servos move correctly with respect to each other.
Now to get the swash moving the right direction with respect to the stick.
Move the aileron to the right. The right side of the swash should tilt down. If it does, fine, move on the the elevator setting. If the aileron control is reversed (tilts left for right stick), go the the swash mix menu and change the Aileron number from +65 to -65. Changing the SIGN of the number REVERSES the FUNCTION (in this case, Aileron).
Move the elevator stick forward (away from you and toward the top of the transmitter). The front of the swash must tilt down. If it does, fine, don't touch anything. If the front tilts UP, reverse the ELEVATOR function by going to the swash mix menu and changing the ELEVATOR number from +65 to -65. Changing the sign of the number REVERSES the FUNCTION.
Move the throttle/collective stick full open (away from you, toward the top of the transmitter). You should get more positive pitch (leading edges of the blades tilt up). If the collective pitch is backwards (you get negative pitch when you command full positive) go to the swash mix menu and change the PITCH number from +65 to -65. Changing the sign of the number REVERSES the FUNCTION.
Playing musical chairs with the servo reversing function at the same time you mess around with the swash mix will drive you nuts.
With a linear 0 to 100% pitch curve, set your collective stick to its midway setting (middle). The three servo arms controlling the swash should be in the middle of their travel range. Due to the way the splines on the servo shafts are designed, you'll have to try different positions of the servo arms on the shaft to achieve this. In addition, you may also need to mess with sub trim to get the servo centered with the collective at its midpoint. The arms are either going to be horizontal or vertical, depending upon servo arrangement.
The swash should be horizontal, and perpendicular to the MR shaft. Adjust the pushrods supporting the swashplate to make this happen.
At this setting, your blades should have ZERO pitch, the washout arms and the pitch mixing levers should be horizontal. Adjust pushrods to achieve this setting. The pushrods up on the head generally go in pairs. Make each pushrod in a pair the same length -- follow the helicopter build instructions to get the proper length of each pair of pushrods.
The swash should be in the middle of its up and down travel distance at this setting. Adjust the pushrods supporting the swashplate to achieve this setting.
So, with a linear pitch curve, at mid collective, the swash is level, the servo arms are in the middle of their travel range, the washout and pitch mixing levers are horizontal, the swash is in the middle of its travel range and the blade pitch is zero degrees (check both blades and adjust as necessary).
At this point you can select the various flight modes you are going to use and customize your pitch curve settings to match the flight mode.
Remember -- to get the servos moving in the correct direction with respect to each other, you use the individual channel reversing menu on the transmitter.
To get the servos moving together in the proper direction with respect to the STICK, use the swash mix menu. Changing the SIGN of the number REVERSES that function.
If you need more overall COLLECTIVE pitch travel, increase the value of the number for pitch in the swash mix menu. If you need less overall pitch travel, decrease the value of the number for PITTCH in the swash mix menu.
If you need more Aileron CYCLIC pitch, increase the size of the AILERON number in the swash mix menu. If you need less Aileron CYCLIC pitch, make the AILERON number in the swash mix menu smaller.
If you need more Elevator CYCLIC pitch, increase the size of the ELEVATOR number in the swash mix menu. If you need less ELEVATOR CYCLIC pitch, then make the ELEVATOR number in the swash mix menu smaller.
At neutral, and neutral trim, the servo arm for the TR is vertical, in the middle of its travel. The bellcrank at the rear is 90 degrees to the tail boom as shown in the manual.
As for the RUDDER setup, when you command a RIGHT turn (will make the NOSE of the heli turn to the right), the servo must PULL the TR pushrod forward, toward the nose of the heli.
For Left turn, the TR servo must push the TR pushrod toward the rear of the heli.
Once you have the servo moving the correct direction, hook up the gyro. Pick up the heli and turn the nose to the LEFT while watching the TR servo arm. The gyro must command a RIGHT turn, pulling the TR pushrod forward, toward the nose. If it is backwards, and if the gyro has a reversing switch, change the direction of travel here. Go back and make sure the rudder stick still moves the servo in the correct direction.
Looking at the heli from its right side, nose to your right, tail boom to your left, the TR assembly turns COUNTER CLOCKWISE. The TR blade on the right is going UP, leading edge UP, control ball link on leading edge.
That ought to get you going with the servos and CCPM installation and setup, as well as getting the TR going the right direction along with the gyro.
When you get around to getting your gyro installed and set up correctly, I can help you with that, too:
Figure out if you are going to use the landing gear switch (channel 5) to run your gyro gain, or if you are going to use the GYRO SENSE menu stuff in your transmitter to set the gain. I'd suggest using the GYRO SENSE menu....then....
A 12-step program (at least 12 things to do to get your 401 gyro working correctly):
Number 1. You MUST apply power to the 401 with it set to Heading Hold mode. If you don't do this, all bets are off on whether or not the gyro will work. The red LED will blink rapidly at power on, then go on solid if you've successfully initialized in AVCS/HH mode. If you don't get a solid red LED on your gyro after initialization, you're in the WRONG mode. Fix the gain setting to select HH mode and try again.
Number 2. Make sure that you've set the mechanical aspects of the tail rotor system up first. Servo centered at neutral, arm perpendicular to the tail boom, and to the push rod. Get the bellcrank at the rear set up per your assembly manual, too. There should be no binding or stiff spots in the mechanics. Fix it before you go any further.
Number 3. Max out your rudder travel endpoints in the TX. This will set the pirouette rate to maximum. If you find that piro rate too hot to handle later on, decrease the endpoint settings as you trim the heli for flight.
Number 4. Set the TRAVEL LIMIT pot so that the servo and tail rotor mechanics don't bind or run into a mechanical stop at either end of the rudder travel input.
Number 5. I assume you have the transmitter rudder direction and the gyro normal/reverse direction properly set to work in the correct direction. If not, fix it BEFORE you fly.
Number 6. Turn the DELAY pot to 0 unless you are using a slow analog servo.
Number 7. If you're using a digital servo such as the 9260, turn the DS switch ON, otherwise, turn it OFF.
Number 8. Make sure ALL RUDDER neutral and sub trim settings are dialed out to ZERO in ALL flight modes. This is easily overlooked, but a must. NEVER NEVER NEVER touch the rudder trim tab on the TX after you've initialized the gyro in HH mode. You will confuse the gyro and the result won't be pretty.
Number 9. When using the heading hold mode, REVolution and ACCeleration mixing must be disabled in your transmitter.
Number 10. Assuming you have the mechanics set up correctly, the travel limit adjust pot is set to prevent mechanical binding at the endpoints, that you are initializing in HH/AVCS mode, you should be ready to actually fine tune the mechanics. Turn on the transmitter, the receiver, and let the gyro initialize in HH mode. Switch the gyro to NORMAL mode, then bring your heli to a hover. Adjust the tail rotor pushrod until you can hold a hover without any stick correction without the heli trying to rotate left or right. Land. Switch back to HH/AVCS mode. Go fly.
Number 11. Adjust your gain for HH/AVCS and Normal/Rate mode based on the flying characteristics of the heli.
Number 12. If you had to do some mechanical adjusting of the TR stuff when in Normal mode, it's a good idea to recheck your travel limit adjustment to insure you don't have binding at either extreme.