wet suits - how much do they help bouyancy?

I have serious issues while swimming. They say that fat is bouyant so I am at a severe disadvantage. 10 years ago when I was in high school they tested our body fat with one of those caliper tests and I was off the chart; below a 10% and I doubt that that number has gone up since then as I'm in better shape now than I was then. I just started swimming about a month ago so I'm still in that sucky phase. The pool mgr says that if I slowed down that I wouldn't be out of breath as fast. I told her that if I slowed down I'd sink, she didn't believe me so I demonstrated it for her and she was speechless.

I've read that wearing a wet suit is a tremendous help in bouyancy but have never worn one alone. I've worn them for waterskiing but that was with a life jacket so I couldn't tell how much it helped. So, my question is, if I were to get a sleeveless shorts type wet suit how much will that help me to float? What about a full length long sleeve wet suit? I'd rather be able to swim without a wet suit but it is so discouraging as I sink like a rock if I don't have my body on a plane like a boat. If I do the dead-man's-float, I sink. the only thing that lifts my spirit in the pool is to think of the expression '$h!t floats' and I must not be full of $h!t like everyone says.