Many questions like this come up every day so many members have worked together to compile a Used Car page found in the FAQ, here is the link for it. Check it out, you can find lots of things there about buying a car I don't know where to get started.

Special thanks to @mountainmanjoe as this used car page is very helpful for everybody. 

But in general, Honda Fits are very good cars. But again, you would want to follow the instructions on the auto buying guide to have a good sense of what you are doing. Off the top of my head, haggle on the price, make sure to have a pre-purchase inspection done by a mechanic, and maintain your car after you buy it.

The best cars to look at are honda civics and toyota corollas, they will cost an initial premium compared to similar cars from other brands, but keep up with regular maintenance and they will run forever pretty trouble free. And civics and corollas are excellent on gas.