Try it! You'll like it.
If you have the opportunity, try a variety of guns first. Frankly, of the guns you listed, none are optimal for clay target shooting. That's not to say that you couldn't use them (unless then range/course has a minimum barrel-length requirement -- some do), but you'll find that the vast majority of folks use long-ish barrels.
For my own shooting, I consider a 28" barrel to be pretty much the lower limit, with 30" or longer even better. Longer barrels (in general) result in a smoother swing and less perceived lead for most shots.
My wife is small, and when she started shooting clays, the overall weight of the gun was far more important than the recoil. She started with a lightweight 20ga, and eventually stole one of my 12ga autoloaders. By the time she "upgraded", she was used to handling the guns and her muscles were built up a bit more. Frankly, the difference in recoil between those two guns, using standard light target loads, is pretty minimal.
Were I in your position, I would hold off on purchasing a shotgun for the time being and see what you can borrow or rent. Try a few different types (autoloaders, pumps, O/U) and see which ones you like and which you dislike.
If you are dead-set on getting something, I would probably recommend the 20ga Remington 870 Express Combo. You get a short barrel for deer-hunting and/or HD, plus a longer tube for bird hunting and clay games. IIRC, at least the longer tube has screw-in chokes, which is good.
Screw-in chokes give you the flexibility to make the pattern tighter or more open, depending upon the game. Skeet typically is best shot with very open chokes. Most sporting clays courses are designed for a slightly tighter pattern (ie. longer shots). And trap is frequently shot with fairly tight patterns.
As far as synthetic vs. wood stocks... I much prefer wood. IMO, they are easier to tweak for an exact fit, and just plain look better.
Good luck! If I were a betting man, I'd say you'll get a bunch of replies to this here thread.
