For Trap, go with a 12. All other things being equal, you're at a 20% disadvantage in the amount of shot (pellet count) with a 20 (Typical 20 ga target loads are 7/8 oz. Maxium allowed for competition is 1 1/8 oz., so that's what they pretty much all are in 12 ga.)
The info on fit above is spot-on. It's like wearing shoes the wrong size...won't be comfortable, and your perforance will suffer if the fit is wrong.
Now....before you buy....try on a few at your local range. Our club has club guns for people to use, but if you go out to your home club on Trap day and say "I'm trying to see what's best for me," The only problem is that you'll have a wide range of (often conflicting) opinions that are all often correct, as much of the game is subjective. I was told, "If you get a REAL Trap gun, you'll be a threat," but my misses are not my gun's fault!
Since you've not decided on a single, all-consuming oving target sport yet, a good quality general purpose 12 ga. ( preferably with adjustable choke) IMO is your best bet. If you decide that Trap is the True Faith (tm), then get a dedicated Trap gun. Same for skeet...
And, speaking as a Cheap Yankee, remember that there are a lot of used "entry level" guns that people have traded up from.
You show Tewksbury as your location, but if you feel like coming down to Southborough Rod & Gun Club
www.srgclub.com I'm sure that a variety of toys will be shared. We're having an Easter Egg Trap Shoot ( see the thread under copetition) this Sunday if you're interested.
Have fun!