Having gone through this same crisis - "What car do I get that won't completely suck?!" - I can tell you that no matter what you get, there are going to be issues. If it's your first car, especially, because trust me, no one's first car is ever perfect. Unless you're rich and your first car is expensive and new...*grumble*
That aside, the car I ended up with was my mom's old car, a '95 Pontiac Sunfire. Yes, it is American. But it's hardly given us any trouble at all. And, for a small family car it has decent space; the rear seats fold down, giving more trunk room - hell, even without folding the seats down it's got a considerable sized trunk. It's pretty much perfect for what I do, which is haul loads of junk - props, costumes, my backpack, the like.
It's not exactly perfect, though. Sunny has her problems. Like one, I'd rather have a manual as opposed to an automatic. Since I got this car and didn't get to buy my own, I haven't been able to learn to drive manual because we still don't have one for me to learn on. My car also has broken air conditioning. Other than that, for a 14 year old car, it's in better condition than a lot of other cars that old that I've seen.
All I can suggest is, if you can, test drive a car before you buy it. Usually you'll know right away if it's something you'll like to drive around constantly just by the first drive - when I first drove Sunny I knew that, regardless of whether or not mom and dad were going to give her to me, she was going to be mine eventually.
And, try not to be so picky, especially since it's your first car and 5K is a pretty mediocre budget to be able to find exactly what you want. So what if one car fits all the criteria but happens to be American? Some older American cars weren't all that bad. I speak from experience; all my life we've had nothing but American cars (a 1984 Jeep Cherokee, 1987 Chevrolet Camaro Z28, 2006 Ford Mustang, and recently a 1995 Cadillac Sedan DeVille), and with the proper care (read: DO NOT OVER-ABUSE) they'll hardly give you any trouble at all.
If you're really set on something not American, though, sift through what you can. Like I said, try and test drive something before you make up your mind. And don't rule out the possibility of a FWD car; after AWD and 4WD, they're the next best thing for wintry-weather. It just depends on what FWD car it is. Some were rubbish, others were alright.
Just make sure you do your research and you should be okay.