1. The barrel just has to be compatible with the slide. If the slide is compatible with the grip module and FCU then you're good (which the GG slide will be). Non-X-series Slide/Barrel combos will work fine with an X-series FCU/Grip module.
2. For 3.9" compact/carry slide you will need a 4.6" threaded barrel for a compensator: P320 COMPACT 9MM 0.5X28MM THREADED BARREL, NO LCI, 4.6"
for a 3.6" xcompact/subcompact slide you will need a 4.3" threaded barrel for a comp: P320 XCOMPACT/SUBCOMPACT 9MM THREADED BARREL, NO LCI, 4.3"
The compact/carry slide plus comp with hang just past the XFull dust cover. The xcompact/subcompact slide plus comp with usually be flush with the XFull dust cover (depends on length of the comp).
Tips on barrel:
- Make sure the thread pitch on your barrel matches your desired comp: 0.5x28mm vs 13.5mm
- Make sure you get a NON-LCI (loaded chamber indicator) if you ever intend to have an optic on the gun. The LCI notch vents some exhaust gas up and coats the optic.
Below is my full sized TXG grip with a sig spectre compact/carry slide (normally 3.9" barrel), with a 4.6" threaded barrel and Harrington arms dual port comp (HC320XL).