Sweet, a little shine time. I am a "Used Car Reconditioning" tech at a large Chevy dealer in my city. Hopefully I didn't miss the party.
You want to buy a "new to me" used car?
Follow these rules/General advice.
1: Buy Toyota or Honda. (or Lexus/Acura, the luxury brands from Toyota/Honda). You'll pay a little more for it, but in the long run it's 1,000,000% worth it.
DO NOT even waste your time on anything else like GM (Chevy, Saturn, Buick, Pontiac, GMC), Ford, Chrysler, Dodge, Jeep, any euro brand (BMW, VW, Etc...). I'd even stay away from Subaru, Kia/Hyundai personally too. These brands do not come close to the higher quality and engineering that is Toyota/Honda.
The more reputable and clean the place is where you buy your car, the better car you can generally expect. I.e..."Buy here, pay here" or "Hablamos ____" car lots is not where you want to be. Go to a dealership used car lot, or CarMax is a really great place. You're going to get better after purchase service from CarMax or a dealer as well, they have reputations to uphold.
There is 3 levels of used cars. A) Certified. B) Inspected & Reconditioned. C) Total crap. Anything that comes into our shop that is to big of a piece of shit gets sold off to buy here pay here lots or auto auctions or places like that.
RUST. Look for it. Walk from vehicles that you find it on. You can typically open a hood and good a decent view of radiator core supports from the top of the vehicle. Rust on the rear frame. Rusted through parts/pieces of unibody/doors/hood/anything.
USED CARS ARE SUBJECT TO BREAK AT ANY MOMENT. This is literally the shop motto and it happens. Yup, nothing like fixing a car, getting ready to back it out, an airbag light is on that was never on before. Shit can and will happen and it's not the fault of the person who sold it to you. It's a USED car. Bad work can be faulted and complained about, bad parts cannot.
Check all power windows from the master switch and door switches and all operate. Check for operating power mirrors. Check all power seats for proper/correct movements. Check power sunroofs. Check power doors of any kind. Check trunk buttons. Check that all seat belts latch.
No warning lights on. Listen for odd engine noises, especially at startup. Check Air Conditioning and Heat outputs. Check/watch engine temperature gauge, make sure no overheating. Look under where the car was parked on the lot for signs of leaking coolant/transmission/engine/power steering fluids.
Obey #1.