Hi there brjss--
I posted this in reply to your other question (under the thread "interesting beginner guns"), but thought I'd move it here to make it easier for your to find. Also I edited to take into account what JLP and WWB have already told you.
First, welcome to shotgunworld! You've come to the right place. Here you'll get friendly and competent advice as well as plain old interesting shooting conversations.
JLPTexashunter has given you a really excellent run-down of the virtues and drawbacks of the various gauges. Each has its particular use and history. There's psychology involved, too. You need to like your shotgun, be comfortable with it, and feel it's the right tool for the job at hand in order to do well. Your shooting instructor was right, but as JLP shows, there's a bit more to it than "the 20 ga just has fewer pellets."
To begin making specific recommendations, we need a bit more information. Do you have any specialized purpose in mind for your shotgun? I.e clays games (trap, skeet, sporting clays), hunting? If it's clays we have many experts on it in these forums. If it's hunting, do you just want a general-purpose gun? A goose / waterfowling piece? Turkeys? deer? Home defense? Or is it "all of the above"--you just want to buy a solid gun and begin learning? Also, it we'd need to know whether you have any particular physical requirements--say a disability--that might preclude guns with heavier recoil, etc.
Post back and let us know and we will make suggestions. I hope you'll consider registering and hanging out here a bit. You can learn alot and avoid some of the mistakes the rest of us have all made :lol:
Best of luck,
Jeff23