I think you've got a good idea of where to start - taking a step back and not solely evaluating that individual car.
First thing to do is to figure out what kind of car works for you. Not necessarily one specific make/model, but a segment of cars (4 door hatchbacks, cars that get >30mpg hwy, etc.). Narrow it down to a list of cars that fit your criteria. Autotrader.com, Edmunds.com, etc. all have good tools for narrowing this down.
Next you want to consider how you're going to evaluate the car. How mechanically inclined are you? Have you repaired moderate issues or brought your car to the shop when something goes wrong? I ask because (as you know with the head gasket issue), the outward appearance of a car can easily mask issues lurking underneath. If you're not mechanically inclined (no shame! it takes a while to get a feel for what thing should look, sound, and smell like), you should consider having any potential purchases evaluated by a trusted mechanic. If the seller is not okay with this, you need to move on.
Take a thorough look at it. Walk around, open all the cubbies, look under the hood, look under the body. You probably won't know what you're looking at but if you find something that is broken or that doesn't look right, ask the seller about it. Take it for a test drive that simulates all the different conditions you drive regularly - leave the radio and climate controls off and listen for anything weird. Any oddities are things you can talk to your mechanic about that might help you make a decision.
if you have the time, I also suggest searching for forums for that make/model - there is a forum for just about every car. Lurk for a while and look at all the problem threads. You'll get a good idea of what other owners think. Search google for "<car you're looking at> problems" and see what comes up - often the most common issues will show themselves this way.
Run the carfax (or autocheck, etc.) but be wary of the information you get. You'll have to pay to do it but you might be able to uncover issues the seller isn't disclosing. Just know that the carfax is almost never 100% correct, and that there are things that can easily be omitted from it.
Finally, pricing - this one's easier but always important to consider. Get the KBB value for that car, look on ebay and craigslist to see what private sellers are listing at, check out dealers to see where they're priced. You definitely want to make sure that it's not priced too low, nor is it priced too high. It will give you a little wiggle room in negotiations if you can show comps.
