Brakes are cheap, probably ~$100 for rotors and pads for the front, and not too difficult to install, though tools are required.
The tranny though, is what bothers me. Check the fluid levels, and take a quick whiff. If the fluid smells burnt, there's a very high possibility something is going wrong. Barring that, check for transmission (and motor oil) service records. Such a transmission will be more likely to fail if servicing has not been done. Go for a test drive, and feel how it shifts. Auto transmissions should be shifting smoothly, but abrupt, jarring shifts can be a sign of trouble as well. In terms of noises, a buzzing, or out-of-place whirring sound is also suspect, though harder to pin down on an unfamiliar car. Just had a tranny go out on my car last Thursday, and god, my wallet cries at night.
Next, I'd definitely take a look at various odds and ends, just to get an idea of maintenance that may need to be done in the future. Are the tires good? Are the CV boots intact? Leaks? etc.
And finally, be aware that even if the car has pristine service records. there's still a chance of something really bad going wrong. That's just luck of the draw.