Ah, a more or less full size sedan. Chopped Merc is a good call, the Fairlanes and Falcons should also work well for this 'recipe'. Kind of rules out the "Deuce Coups", two seaters and other 'exoctics'.
A solid and interesting question and SHOULD stay within a reasonable budget (what with the kids and all).
"Shoe Box" cars are in the running, but I'm a Ford man! Mid 50's Ford comes to mind as a car I'd like to see as a 'Hot Rod'. Maybe lowered all around (handling), no chrome, perhaps bumpers painted same color as car, 17" rims? Go 'different', go FORD!