1) Your library has access to the Consumer Reports car rankings. They aren't the bible but they're worth looking at. You'll get a sense of what people report a lot. You will also see a bunch of people bellyaching about everything under the sun.
2) Edmund's lists the current prices for everything local to you, regardless of what the dealers are getting. Get a sense of "stuff from (1) that interests you" and "stuff from (2) you can afford" and build a short list.
3) Figure out what you can spend. This may include approaching your bank, other banks, local credit unions, etc to see what sort of loan you can get. Money is stupid cheap right now and it just gets cheaper when dealing with a new customer and a new loan. I was at Washington Mutual when I bought the Dodge. They offered me 12%. I happened into QFC and Alaska Federal offered me 2.3%. The loan officer actually got mad at me because the bank was making like $180 for the life of the loan.
4) Cross-reference (2) with (3) and check out Ye Olde Craigslist and Ye Olde eBay. A few details:
4a) Banks will not loan any money on a private party seller. If you're going to borrow money, you're buying from a dealership.
4b) Banks will not loan any money on a vehicle older than 7 years old.
4c) The prices dealerships list are imaginary. They have no bearing on reality. You can see what the "avg trade-in" on any car you're interested is likely to be and if you're patient, and if the stars align, you might get close to that. I went to see a car listed at $18k. I walked off the lot at $16k. Two weeks later they offered it to me at $11k. Trade-in was $10k. When I bought the Benelli (a motorcycle, but still) I got the bike for $300 more than they took for trade-in. Just recently I went to look at cars listed for $32k that had mystically come down to $21k as I walked off the lot.
5) You now know how much money you have, an approximation of how much money it will take, and a few choices as far as what seems interesting. NOTE THAT SO FAR the only in-person stuff you've done is getting the loan pre-approved. But now you're gonna go drive some shit.
6) BE VERY CAREFUL to read any paperwork they put in front of you to test drive - I found a couple dealerships that tried to slide me "agreement to buy" paperwork at over the sticker price because used car dealers can be extremely shady. But once you've read and made sure you're okay, drive it all. Drive everything. Drive multiples of the same car. Find the one that tickles your fancy. The $18k car that became $16k that became $11k wasn't nearly as much fun as the $9500 car that became $9200 that I'm still driving 14 years later. The $32k car that became $21k wasn't nearly $21k worth of fun so I walked away. Now, repeat after me:
7) "I never buy anything on the first day."
This is your maxim. Repeat it like a mantra. They will pressure you. They will bombard you. They will do anything they can to get you in their pocket. Used car dealers are the kings of high pressure sales. Don't fall for it. "That's a nice watch" they will say, which primes you to think you are rich and deserve a nice car. "I never buy anything on the first day." Once your'e back in your beater the reality distortion field dissipates and you didn't pay more than you wanted and now they'll call you (you can give them a fake number but a real email) to try and get you back into that car. Ignore them. They are vermin.
8) Unless they have the car that you actually want. Now ask them if you can borrow it overnight to have an independent mechanic look it over. If they balk, walk. If they don't, find a local mechanic you like and pay them the $150-200 they'll want to inspect the car. This will be a compression test, an OBD2 reading, an assessment of belts, hoses and the like and the basic surface-level stuff that will tell you if it's been abused.
9) The car won't go out the door unless you have an agreed-upon price. Basically at this point you're good if the car is good, they're good if you're good, the bank is good if everyone else is good and you're ready to pull the trigger.
10) Sign and drive.
It looks like a lot. It's not. 1-2 is a couple idle weeks, 3 is a couple days, 4-7 is whatever it takes to find what you want, 8 is an evening and 9-10 are an hour and a half or so. You're basically looking at a day or two on either side of test-driving and trying not to catch leprosy from used car dealers.
And frankly, I enjoy test driving and there is no slower-moving, slack-jawed, unredeemable group of fuckwits than used car dealers. Abuse them with impunity and have fun.
PROTIP I've gotten a Honda Fit up to the door sills in a river multiple times with no ill effects and have yet to find a national forest road that I couldn't get a Dodge Stealth up. the Jeepy shit you really only need for unimproved roads. Or deliberate dumbness. Think Elbe Hills is about an hour or two from you. Do not attempt in a Impreza.