You can rent shotguns at most ranges. That way you can try out different types. If you have a shotgun, make sure it has an choke that's open enough to not handicap you. For skeet, it should have a Skeet, Cylinder, or Improved Cylinder choke. For trap, Modified, Full, or Improved Cylinder. Trying to shoot skeet with a Full choke can be done, but the tight shot pattern makes it a lot harder to hit the clays. If you want an all-around gun, the 12 ga is the most popular, followed by the 20 ga. The 20 ga. will have a little less recoil, but doesn't throw quite as much shot as the 12 ga.
Read the forums, shotgunworld.com is the best....
First off, welcome.
I use this link to locate places to shoot: http://www.claytargetsonline.com/index.php
As for the gun, use what you own. I've seen kids do awesome with a .410, and adults with their $10K custom firearms that can't hit a barn at 10 paces. It's a game of skill.
Don't be afraid to ask questions at a club/range. The kind of response you get will tell you all you need to know about getting involved with a certain group.