Aw, come on guys, help the newbie out. You were a newbie once too.
Don't wear a wet suit. It's a pain to put on & take off, it's expensive, it's uncomfortable, and it makes rolling harder.
Whatever you wear under the dry top will likely get wet. Polar fleece should be OK, but it will hold quite a bit of water and it may be too warm on many days.
Paddle shops will show you the nylon mesh shirts sold for the purpose. It's like fleece, but a thicker weeve so it doesn't hold as much water.
Get two: a thin and a medium thickness. On really cold days, you wear both.
Here are some links