brokenwings16, I wanna be clear here... I respect both foreign and domestics, new and vintage. I have owned and driven everything from Fiats and Lancias to Corollas to muscle cars. My Mach was my first car, and it still owns my heart, even if its not the fastest or best handling. But I also love Initial D, my brother is building doing a JDM Silvia conversion of a 240SX, and I've been eyeing an '88 323GT turbo lately.
Now, you're in a tough spot looking for a decent fun new car for under $16k. You're not gonna be able to touch a new RSX (type-s or otherwise) for less than $19k, and under the $20K line, you're probably only really gonna find wannabes. However, if you're willing to buy used (even just 6 months to 1 year old), then you're options will open up a bit. I'd look for a used base RSX or Civic Si, Matrix XRS (180hp/6 speed), Focus SVT (170hp/6 speed), Neon SRT-4 (215hp/5 speed), Tiburon GT (170hp, 6 speed), Sentra SE-R Spec V(175hp/6 speed), VW Jetta or GTI w/1.8T turbo (180hp/5 speed). All of these should be right around $16k used, and all of them have plenty of options for upgrades using that $5k you mentioned, but none of them are gonna make it into the 11s for that little. 14s probably, 13s maybe, but 11s... simply no way! Even with nitrous.
Now, that said, here is something to think about. For the same $21k you'd be putting in those cars to run 13s, you could buy a 1 year old Mustang GT for $18k (which can run 13s out of the box with the right driver), and spend the extra $3k and get the car into the high 12s. There is still something to be said for Domestic V8s. And to echo what others have said, $21k can get you a very fast and capable vintage car that will maintain its value better than nearly anthing you could possibly buy new. That probably doesn't mean much to you now (you're probably thinking cars are pretty disposable), but as you get older, it might.
One last thing... if you're serious about twisting your own wrenches, consider going with something like an S13 Nissan and doing a JDM swap like my brother. He bought an '89 240SX with a blown head gasket for $1200 and bought a JDM Silvia front clip for $3K, a LSD for $300, some various parts for the conversion, plus
Eibach springs, a
suspension rebuild with a new rack&pinion. It'll probably run low 13s and handle great when he is done and he'll have less than $7k in it total. Just a thought...
Hope this helps... Good luck with whatever decision you make.