Most rides are indoor, I would probably say a safe bet would be DHS. The problem with AK is well all the animals won't be out and it is a very "exposed park" imo, what I mean by that is just very open and not a lot of areas for quick cover. I would say MK could be a potential canidate too but you may miss BTMR if it is too bad outside maybe even possibly Splash? I have been to Epcot in the rain and it was miserable, granted we didn't have a poncho or umbrella so that was our mistake.
In terms of gear I would bring ponchos/umbrellas and warm clothes of course, you don't want to make the mistake of not bringing those and then having to pay extreme prices for those items in the park. All in all from my experience it is nice going to the parks in the rain, it deters most people from going and sometimes you can get on a lot of good rides! (indoor of course)