[MrPbody]

In today's market, the most affordable cars that meet your needs are the GM G-bodies, '78-'87. Those are: Chevy Malibu and Monte Carlo, Pontiac Grand Prix, LeMans and Grand Am (rare), Olds Cutlass, Buick Regal. They have good frames and suspensions that lend themselves well to high performance upgrades. Parts are readily available.
All the necessary hardware to install a big block Chevy in a Malibu is available in "kit" form. If you choose the Pontiac, headers are available through Indian Adventures. The bigger engines from Olds and Buick would be an exercise to install.
You'll get the best results from a big engine if you stick with the Chevy or Pontiac. The small block Chevy should not be discounted, as pound for pound, dollar for dollar, it's pretty hard to beat the SBC. If you want more than 500 streetable horsepower, though, the bigger engines are better, as they can make that level of power at a much lower level of "tune". 454 or 455P (or variations on the theme) are "king" street motors.
Of course, you could always go the Ford route... Rustangs are pretty cheap and available. There are kits to put the 429/460 into the Fox body. ANIMAL!!!
The Dodge engines are excellent, but finding a suitable body to put them in has become a lottery of sorts. Cudas, Chargers, RoadRunners, etc. have all gone nutso in price (like the GM muscle cars). I suppose you could put a 440 in a Duster... But then you'ld have to be seen driving a Duster (ICK!).