Get a used a-cat to start with. They are light.
What is the use of a single handed cat that is best moved by 2 people?
Turning turtle isn't really a problem. Cats can be righted from a turtled position. Also just swimming the bow around as soon as you flip will eliminate the worry of turtle.
1 exception to that statement is shallow water. If your mast tries to turtle, and drives into the bottom, it could bend or break. So, in shallow water, get to swimming that bow around asap.
The more you have to spend, the lighter and newer the boat you buy can be. For me 300# is a strain to pull up the beach by myself.
Basicly they all work and are faster than most monohulls, so for lake sailing any cat is fine.