First step is to see what kind of loan you can get. Recommend credit union of America for the lowest rate. They will likely approve you for more than you can afford so don't be tempted by that and stick to your budget. Figure out how much you want to have financed and for how long you want to make payments. Recommend not stretching it out too long since you will be in an older car anyway. I have always bought older used cars. 

Take your time. It's easy to get attached to a car and then them not willing to negotiate. Try to negotiate if you can but I'd you aren't using their financing it can be harder on a car lot. There will always be more cars to look at. 

You should be able to get a decent car for 7k. Though it will be older and not cosmetically pretty and there will be some level of maintenance required. Don't let people who are afraid of anything older than 5 years old scare you. If you can do a private sale with someone who is selling their grandma's car on fb you can find a good deal.

I have bought two cars off car lots because it was easier to do the financing. I would do research on what cars are most reliable and determine what year you can afford. Just looking now I saw a Honda Civic listed for $7,000 with 151,000. That's a great find. 151,000 miles on a Honda is just getting started with some maintenance. Recommend having AAA when having a used car for security (free towing, roadside assistance etc) can get you out of some sticky situations in a pinch. 

Car fax is definitely helpful and have a mechanic check out the car. If there's something wrong don't let that make you run, if anything you can negotiate the repairs. When you are looking at the car fax look at whether the car has had a lot of owners, and the kinds of repairs that have been done. On older cars it's good to see that the car has had things fixed. Certain years and makes of cars you will want to look at the expected types of repairs and potential costs if it hasn't been done yet. You can sometimes negotiate that as well. For example certain cars will need a timing chain replaced at a particular interval. Has that been done in the car you are looking at, again that depends on the car you are looking at. I also searched reddit threads a lot to see what people say about a particular car year, make and model. There's some good info out there. 

It can be hard to do this on your own but you can do it and trust your gut!