I can't vouch for Carmax because I always like to buy local and go look at and drive the car. If they are giving you a limited warranty, I'd take it. IMO, they are just going to take it to the dealer and have it safety inspected (which you can do yourself with any used car for $100-150, I do more often than not).

Yes, these cars are pretty easy to maintain and aren't all that expensive for the basic maint stuff, so I think they make a great first car.