Or if going TruTrak, Aspen E5 is the better bet as they are working together on integration. The G5's have limited integration and Garmin has no plans to help the TT guys, but that's another discussion.... The TT is a great affordable and easy to install autopilot, I highly recommend.
As far as STC/AML and 337.... Yes, you need a 337 when installing STC items. In the 337 you need to reference the STC/AML number, install manual numbers, the fact that you put the continued airworthiness and poh supplements in the proper places (I even include their part numbers in the 337 for all the paperwork just to be thorough). You also list the serial numbers of stuff coming out, stuff going in, etc....
I guess it is basically because an STC by nature (supplement to the original type certificate) means it is a major alteration....
The STC just gives permission to modify the airplane per the install manual.
A lot of guys think of the 337 as a field approval for a non stc item. A 337 is part of a field approval, but isn't one in the same. A 337 is legal if signed off by FSDO as field approval (good luck on getting that) or via STC.
That being said, I'm sure I've wasted a lot of time typing out some great 337's that NEVER EVER get looked at over at OKC, but they are good for the logbooks for any future owners of the airplane.