I really wish I'd seen this sooner; I'm a hard-core car guy. In college I had a huge stack of car magazines under my bed (which my friends referred to as "car porn"), and several subscriptions. I got Top Gear from the UK (best show ever!) and generally obsessed over cars I will never, ever get the chance to drive. I've even exchanged emails with the makers of cars such as the Ariel Atom before they became popular/expensive. What I'm trying to say is, I care too much.
That said, I have to agree with most of the advice here. Stay away from old Jeeps with a lot of miles, they don't last much over 150k in general and they aren't the cheapest things on earth to repair. Also, something to consider when cost is an issue is mpg, and sadly most older jeeps just don't have it in that regard.
Something to remember is the incredible value of a manual transmission. They are usually cheaper, they are easier to maintain as long as you go easy on the clutch (good technique is easy to learn, and saves you tons of money) and they get better gas mileage. Plus, they are more fun to drive and give you more control over the vehicle; very useful in dangerous situations if you know what you are doing.
Stay the hell away from Saturns for both reasons stated; they are cheap cars in every way (meaning you don't pay much for them but they don't last long) and the company is defunct. My Dad and I always called them the perfect American car; cheap, plastic, and disposable.
On top of this they just aren't safe, and that's important for a first car.
I will disagree with Jor and say that, with careful research and a car inspection, you can do really well with a good european car, particularly Saab's or Volvo's, but also Volkswagon's. Some models are better than others, but Saab engines in particular will go forever. Most of the Saab owners I've known have finally junked the car because the body gave out. The engine was well over 300k miles and still running fine (assuming proper maintenance, such as regular oil changes). I've heard of Saab engines beating 500k miles before finally dying. You can't beat the Swedes for quality engineering, and the German's aren't far behind. The fact is, however, that Jor is right in that when things DO break European cars are much more expensive to repair. This is particularly true of english cars (stay away from any British car built before about 1990, especially if Lucas had anything to do with the electrical system). Also true of any euro sports car, particularly those built in Italy; just too danged expensive to repair.
Japanese cars are the ballance point, not the cheapest or the best built, but the best value for your average run-of-the-mill car. However, not all Jap cars are made equal. Toyota's are the most consistent, and you can't go wrong with a Camry; it's reliable, safe, and get's great mileage. Just a great car. I highly recommend a 6 cylindar Camry if you can find one; the older four bangers tend to be a little gutless, which is really my only complaint.
Honda's are reliable, but they tend to be uncomfortable and they can have poor handling characteristics. This is particularly true of the two door Accord's. I've hated every one I've driven (three I believe). They are painful to ride in for more than an hour or two (unusually so, for those smart-mouths who would say any car is painful after that long
) and they don't have as good of a safety rating, mpg rating, or really anything else as the Camry's. If you ARE going to get an Accord test drive it, have it inspected, and for God's sake get a four door.
As a side note on Honda's, don't by a CRV. They aren't great for mileage, handling could be better, and as Car and Driver said so well they would have trouble towing a box of donuts on a level road, let alone a small trailer. Just don't go there.
The BEST Japanese car company available in my opinion is Subaru for a variety of reasons. First, they hold their value like crazy. This makes them expensive initially, but they are also still worth most of what you paid for it when you go to sell it (if you don't love it so much you drive it into the ground!). They are reliable, they are cheap to repair, they have great mileage, they are comfortable, they have well aranged interiors both for passengers and for cargo. Best of all is the drive train. First of all, the engines are the best maid four cylinders around; they are flat-fours, what Subaru calls a "boxer" engine. This design is used in most general aviation aircraft and provides a lot of torque without sacrificing acceleration. You don't get as much in the high-end usually but I'm assuming you aren't looking for a street-racer.
If you are, Subaru's can be modified like crazy, they are sick tuners. The other great thing about the drive train in a Subaru is that they are ALL "all wheel drive". This is important. They are not 4-Wheel Drive, they are ALL Wheel Drive. All Wheel Drive is a much, much better system, like infinitely so, but I won't go into details here. If you want a reliable all-wheel-drive car that is cheap to maintain, get's good mileage, and is safe you can't go wrong.
Best piece of advice I can give you is that you should do your research! Consumer reports is a great option and definitely worth the subscription fee, you get a wealth of useful information that is well organized and easy to understand.
Also, don't fall for that car that is so cheap you can't believe it. It's easy to buy into a lemon, or a car with high maintenance costs, frequently needed maintenance, or a poor mpg rating. Better to pay a little more and get a reliable car with good mileage.
Finally, safety is extremely important for a first car so keep an eye on that. Sorry this is so long winded and disorganized! It's late and this is all off the top of my head so bear that in mind. I am more than happy to take on specific questions.
Oh, and have fun! Cars are awesome.
