It sounds like you're interested in paddling on the lake, which is great, but eventually you're going to want to do whitewater because whitewater is where things start to get fun in a kayak.
My advice would be to get an older model whitewater boat like a Pirouette or a Dancer. They work great in flatwater cause they're fast [long straight hull] and are awesome beginner riverrunning boats as well. They are easy to roll and you can get them used for cheap [$200-300]. Remember you'll need to spend money on a paddle, sprayskirt, pfd and helmet too...
Definately don't buy any boat new! They last forever. I have one boat that fell off the van into a Talus filled ravine at 45mph... it was fine!