A low mile 04 with the 5.7 would be every bit as good as an 05-06 with the 6.0 if you plan on modding it. They are great, great cars. Quality well above even some of what GM makes now. You have a gen III motor so power is reliable and way too easy, t56 is almost bullet proof, great interior and people can say cavalier all they want when they're eating crap from your tail-lights.
I went through this recently.. like said above the only competition in the price range is either a s197 mustang, 350z/g35 or maybe a low, low mile 4th gen fbody. 03-04 Cobras are still gonna be up near $20k without a salvage title and good fcking luck finding one anywhere remotely near stock. Maybe if you're lucky you could find a decent GTO near $15k.
From what I've heard 350z falls the hell apart, dunno how that translates to g35 but seeing how your average Infinity owner (doesn't) take care of their care I'd stay away.
S197 Mustangs are fun as hell. The chassis is amazing for what it is, they just handle really fun, toss around surprisingly easy and there is a massive aftermarket. But they are slow as hell stock- like stuck between lt1 and ls1 fbodies. But a whipple can change that all. They also hold amazing resale value for as mass produced as they are.
You could get a 4th gen fbody, not as nimble or fun feeling but still huge aftermarket and you can make power stupid easy with just a cam swap. But then you'd have to grow a mullet, fck your cousin and replace all the electronics twice a year.