If you stay in the southern US a daily driver 2002 is a practical possiblity. If you end up in a big northern city then you probably are going to want something to back up the 02.
In that price range a VW Golf or Jetta is an obvious option.
Also a well kept e30 would be very reliable, RWD and a great car. Get the 91 318is and it will get about 25 mpg too.
not so obvious (low budget)- 2002-2005 Neon R/T. Not the turbo SRT but the sport package model. You can easily find a nice one in the lower end of your price range and Dodge did a good job on the suspension. Decent sport seats. 16" wheels. It actually reminded me a lot of an E30 except for the front wheel drive. Pretty basic as far as options, but great to drive. Insurance was pretty reasonable too (unlike the SRT4). And before I get a bunch of responses laughing at my suggestion of a neon, please remember he had an Oldsmobile on his original list.
not so obvious (high budget) The new Mazda3 is my vote for the modern incarnation of an e30. Great handling, well built, cool interior (you gotta see it at night with the gauges lit up). I'm not sure if the early ones have depreciated into the top end of your range, but if they have, definately worth a look. A lot more amenities than the neon.
Stay away from the Audi (the Jaguar of German cars in my opinion - they break too often and are too expensive to fix.) Forget about working on them. Audi/VW loves to invent special tools for their cars.
You can easily get a well kept e36 BMW in that price range. I just find them boring. E36 M3s are starting to fall to around 10k, but they are generally high mileage rats. And you are back to killer insurance if you are in your early 20s.
Good luck!
P.S. I've had every car on this list except the Mazda, plus the Mini and Audi from your list (although it was an A6). If I was going to adhere to your budget and more modern 2002 principle I'd go with the E30 318is. Blast to drive, great forum (m42club.com), easy to work, very reliable, etc, etc. I've have one and its the best e30 after the M3.
If you simply asked me what would be a good daily driver if you were to keep your 02 as a toy car then I'd say check out a Scion xB. Sporty handling, great mileage, and unbelievably practical. It has limosine like seating space and you can fold the seats down and pack it like a suburban. I have a trailer hitch on mine and tow my fishing boat to the lake, and use a utility trailer to haul my lawn mower in for repairs etc. Plus its a Toyota so it never breaks.