I've been in your shoes several times....well, I was until we had 3 children...car budget is now dead.
I ran the spectrum like you're doing....looked at everything from M5 to Esprit to Elise to 911 on and on. Here are the ones I actually owned:
FFR Cobra
C5 Vette (twice)
Viper GTS (though it was over the $25 budget, but you can find an older roadster for that price)
GTO
Heavily modded Mustang (several times)
From your description, I'd go C5 Corvette. $25k will by you either a mint low mileage unmolested car, or a very nicely modified car. I had a '98 that dyno'd at 470rwhp and I got it for somewhere around $18k...of course that was 3 years ago. The 'Vette isn't ultra exotic, but you'll get your share of looks. It's fast as hell, handles well, responds to the right mods really well, and is comfy enough for daily use. If you want to go more exotic, go with a completed FFR Cobra. Every time you stop for gas, be prepared to spend 10 minutes answering questions.
It's a blast to drive, and since it uses Ford parts, their cheap and easy to come by. A very "raw" driving experience, but that's part of the charm.
BTW - current daily driver, now that the toys are gone, is an '06 Miata....