I get my suits from surf shops. Dive shops have them as well, but try to get one that is made for surfing. There no buckles or snaps (they would ding the surfboard) and the zipper is on the back with a long lanyard for pulling it up and down by yourself. Academy sells a cheap model which should work fine for doo-ing.
Wetsuits will still be cold when you first get in the water, but not quite as cold as the water, since the foam rubber suit will be warmed by your skin before you get into the water. It is basically like wearing a sponge. When you first get in, the cold water absorbs into the suit and leaks in to your skin. Then it constantly recycles fresh water in, but slow enough that your skin warms it to a reasonable temp. Your hands, face, and feet will still be very cold, especially if the wind is cold blowing on you.
You can buy gloves, booties, and face mask if you get really hard core or if the weather gets really cold. By then, I switch hobbies to something dry, like driving my hot rod, reading in front of the fire place, or if it has to be wet, sitting in my hot tub.