Lateral-g project car on a budget.

[JayR]

Since this is a budget, I'd keep it on the frame and since the emphasis around here is on turning and stopping, I'd start pricing bolt-on suspension upgrades and maybe a junkyard brake swap from late F-body or Corvette. Then some bolt-ons for the motor like i mentioned before, carb/intake/headers/exhaust
Maybe check the classifieds here and at "the other site" for any A-body stuff as well as Olds forums for motor stuff.
Doing one mod at a time and following it through would keep it affordable and from being torn apart for months at a time and make it interesting to follow along with. You could also test-drive and evaluate each modification.

Since it's a Cutlass S, how about S Curves for a name?