MongooseGA said:
Does anyone know of a good, solid, reliable car that can be fun to drive? ...
-Insurance needs to be as reasonable as possible.
Like TW85 HHI said. Any late-model German luxury sedans in your price range are likely to have high mileage and been driven hard/put away wet. Good and solid, yes. Reliable? That may be up in the air. Perhaps the price is low for a reason... It does you no good to have a stylish, prestigious Euro-car that spends one week out of every eight in the shop because the previous owner didn't treat it right. BMW parts are EXPENSIVE.
I think you're on the right track with the RSX. Despite the fact that I am a die-hard Toyotaphile, I think Honda has a great product line and manufacturing ethos. Finding a low-mileage one in your price range may be difficult, though; a $14.9K RSX may not be in exactly the best condition. You may want to consider:
1) Mid-late '90s Acura 2.5TL. 4 doors, decent trunk, Made in Japan quality, useable (by real adults) rear seat, sweet Honda double-wishbone suspension at all 4 corners, longitudinally-mounted 176-hp inline-5 engine, and I think a number of them were available with a 5-speed.
2) 1994 and up Infiniti G20 Touring Edition. This spans 2 model generations, with the newer body style appearing in 1999, if I'm not mistaken. 4 doors, brilliant handling, well-bolstered sport seats, a little smaller than a TSX. Tough-as-nails SR20DE engine. Lots of mods available, predictably.
3) 1993-94 Toyota Camry SE. The 5-speed was available until it was replaced with an automatic-only in 1995. 185 hp, AND the shorter final-drive ratio from the Lexus ES300, enabling mid-15-second quarter-mile times. Note, the 5-speed/V6 combo reappeared in the 1997-98 Camry, which looks particularly handsome with the TRD bodykit. All the room you'll need.
4) Mid-90s Lexus ES300. Like driving a really nice Camry that girls your age would like. No 5-speed, though.
5) Mid 90s Lexus SC300 5-speed. Rare rare car, they are usually found with autos. However, I hesitate to recommend the more technically complex Lexuses to people on a restricted repair budget, because even though the cars are reliable (engine/tranny-wise), the little eelctrical repairs will KILL you at the Lexus dealer. (e.g. new power window master switch panel, $275.00)

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6) Toyota Celica, 2000 and up.
7) Any adult-owned, maturely-driven, low mileage mid-90s N/A Z32 or Supra. I'd stay away from the Turbos, for reasons of expense and technical complexity. Supra might be out of range, price-wise.
8) S14 (1995 and up) 240 SX.
9) After all is said and done, it's hard to beat the older double-wishbone suspension Hondas/Acuras. Especially if you're going to drive "spiritedly"/autocross. A late 90s Civic or Integra, or even an Accord, is a satisfying car to own, and will have a minimum of maintenance-related issues. Plus, most will be cheap to insure for someone in your demographic (unless you're looking at an Si/GSR/Type-R).
Sorry to chime in so late, and good luck with your hunting!