Angel Eyes,
Conerning your question about think or thin wheels, I think you should get a bike with thicker wheels. I first rode my (first) roadbike last December and had some difficulty riding it straight and getting the balance right at slow speeds. In my case, I already knew how to ride a bike...
Maybe you should get a mountain bike since it has thick wheels and would be of good use in the future if you become interested in mountain biking.
Just my $.02
Goodluck!