We just bought a used car yesterday for DDs. They need it for work (6 people, 7 jobs, no transit and down to two cars) and college in the fall.
Consumer reports is your friend! The magazine is only a few dollars and worth every penny.
Before you shop, you have decide a few things.
First, your budget. It's really easy to pay too much, especially if you are in a rush.
Second, how much car do you want? We wanted a car with an expected life span of 4 to 6 years before major repairs would be an issue. For us, that meant good body condition as Canadian winters are hard on cars. It also meant moderate mileage, as the DDs will be putting in some road time to and from school.
Is climate an issue for you? In our area, a car without a functioning heater is not drivable in winter, so that's a must-do repair, and cost must be factored in. I'd guess other are parts of the US where A/C is equally a safety issue.
I'd start looking at used car sites, kijiji etc to get an idea of of used car prices in your area. Find something in your price range and then check the reports on that car. Decide if the down checks are something you can live with.
In our case, the brakes were rated a bit low, but we were okay with the idea that we'd possibly have to budget for repairs on a shorter lifespan.
Talk to people! Ask your friends and family what they are driving and what issues they are having.
We stayed away from makes we haven't been happy with and it reduced a lot of stress. I ran into a friend who is an apprentice mechanic and asked about his car. Based on his comments, we took that model off the list.
By the same token, we have family members who have had the same car for years and have been very happy. That car was also highly rated and wound up at the top of our list.
Listen to your instincts about the person selling you the car. Our salesman was so low-key it was almost off-putting, but he did not push. And he won huge points when we wanted to test drive one car and he said "I wouldn't sell you that car. It has a bad shimmy in the front end. You're buying this for your kids, and I wouldn't let my kids drive that car." Given that the car had a dead battery and the girls hated the body layout, we skipped it.
Get the car checked. We bought used from a dealer. We knew the price might be a bit more than on a private sale, but for us the trade-off was that we didn't have to worry about mechanical reports, safety inspections or doing the title search. All that paperwork was included and we didn't have the hassle. (Like you, we were in a hurry).
Don't forget a title search! It will tell you if the car has been written of and rebuilt (major safety red flag!) or if there any liens or claims against the vehicle.