Don't ask us, ask Remington!
http://www.remington.com/products/accessories/gun_parts/remChoke_tubes.asp
FULL REM™ CHOKE TUBES
• Delivers tight, well-placed shot patterns when shooting between 45-55 yards
MODIFIED REM™ CHOKE TUBES
• Versatile Rem™ Choke that delivers wider shot pattern for shooting at 25-45 yards
IMPROVED CYLINDER REM™ CHOKE TUBES
• Short-range choke that delivers wider shot patterns for game within 35 yard range
My recommendation: Improved Cylinder. And try both barrels. The short cylinder-bore barrel might work surprisingly well for some shots, though the 28" barrel will have a smoother swing and natural follow-through. But if nothing else, learning to quickly acquire a target and point-shoot accurately with the short barrel will make you a lot more effective should you ever have to use it to save your life. And practicing with the long barrel is invaluable if you want to hunt or do any more formal clay shooting.
American Trap birds come out of the house 16 yards in front of the shooter and fly at 36 MPH, give or take. And IC works just fine for that, though I prefer Modified for trap singles.
For hand-thrown targets that start flying right near the shooter, IC is the only choke that makes sense.
If you want to practice precise shot placement, use a Full. You can tell where you hit the target (or if you miss -- the clay bird will move away from the shot column flying by) with a Full choke, so you can practice hitting it dead center. But it won't be as easy to hit, so if you're starting out, I'd enjoy the IC until you're bored. Then go Modified and then Full. If you're really feeling cocky, get an Extra Full or a Turkey choke. Good luck!
Have fun. Shooting flying stuff is highly addictive.