Pow hound hit the nail on the head. Although nobody seems to agree with me, I suggest getting a very tippy playboat and paddling parks and Class III rivers constantly. I swam, a lot. But, I learned balance, edge control and bracing quite well.
Some thoughts on gear:
Helmet - get a WRSI, just that simple
Paddle - don't spend a fortune. You will loose it. Either get one of those cheap aquabounds, or better yet get a deal on used werner. Getting a used AT paddle is asking for a broken paddle.
Dry-top: Get a nice drytop. It will make a big difference in your paddling enjoyment because you won't get cold. Expect to pay $250 min.
Boat - I really think you can skimp here and save some big bucks. A proven older style boat playboat can be gotten for about $250. Some suggestions: Dagger Crazy8, Pyhrana S-6 (not the S-6F)(my personal favorite of the oldies), Jackson fun series, wavesport ezg series. There are lots of others obviously.
Skirt - Whatever. Just make sure it fits your boat and has a loop you can pull to swim.
Throwbag - Just get one. This will be a long-term investment, so like the helmet, dont' skimp.
Noseplugs - For union, of course.
PFD - Something whitewater kayak specific
This looks like a pretty good deal: Complete Equipment Package Bargain - Mountain Buzz Gear Swap