If you are looking for something reliable and economical, steer away from rental car places the the korean cars for the time being. Your best bets are cars along the lines of a well maintained:
1. Honda Civic/Fit/Accord
2. Toyota Corolla/Camry
These 2 brands and the cars listed have proven to be consistently the amongst the best in their class new and pre-owned. Regardless of what you buy, ask for proof of servicing (oil changes, etc). Take someone with you that knows a little something about cars. Take it out on the highway for a drive and make sure there are no vibrations in the steering, transmission or brake pedal. Test all equipment (seat belts, fan, heat, A/C, radio, signals, lights, etc) to ensure everything is working. Check the condition of the wheels/rims (make sure tires are the same brand/type and correct size. Run the car through a car wash to check for leaks in window/door seals and check under the vehicle in addition to the condition of the engine bay. Spot check the oil...if it's black walk away. Oil should (in most cases) be a honey brown when newer.
If you have any specific questions, please pm me. I eat sleep and breathe everything automotive. I've owned around 30 different vehicles, maintain all of mine, build and even race a couple of mine.
Ryan