If you really hate being out in the rain, like my DH, the best park is probably Epcot because everything is indoors. You just have to go out in the rain to get from one building to the other.
MGM would be my second choice, followed by MK.
The main problem with MK is that some of the rides are outside uncovered (big thunder mtn, splash mtn, dumbo, aladdin, jungle cruise, etc.) If these are important to you, MK might be best saved of a non-rainy day.
If wearing a ponch and getting a little wet does not bother you, go to your favorite park. I agree with kilee. The lines will be much shorter for the most popular rides and most if not all of the attractions will be open.
AK is the most difficult park to find a place to get out of the rain.