To confirm alaneapen's statement, Eevee can be found in the Mysidia Railcave on windy nights between Aya and Serra. You can get the Water Stone while doing the Gang Quests.
True, Muk's Special Attack is a bit meh, but if you can be bothered to breed Curse and Shadow Punch onto it (Dusclops -> Grimer), then it makes for an offensive force and bulky tank with Gunk Shot (learned at Level 40) and Brick Break (given along with the 10th Badge, if you're still using Muk then). It's also easier to level up later on, as its experience type is medium fast as opposed to fluctuating.
You should also introduce yourself at the Grand Hall, since you're new here.