For me it's pretty simple. I just want a performance car that emphasizes the driver-car connection. This means I want a simple, raw machine. I'm disappointed by the proliferation of fancy gadgetry and 'look ma I am giving the illusion of being a competent driver' technology.
-light weight (the new M6 is over 4000 pounds! I would probably draw the line at 2500.)
-drivetrain layout negotiable
-rear wheel drive only (all-wheel-drive diminishes the purity IMO)
-no ABS
-no traction control
-no stability control
-no launch control
-probably no power steering
-manual transmission
-probably naturally aspirated
-'enough' power, which probably means anything over 300 is fine
Probably why I'm in love with the GT40 replicas. (Though the Ferrari supporting part of my brain is not happy about this.)