These cars are LIGHT (well, supposed to be, anyway), and with, for example, a McSorely chassis, you'll find that with 1" tube the frame is VERY strong. It gets its structure from diagonal triangulation of the tubes, and it's much stronger than it needs to be for the weight (most are 1300 lbs. or less - ours will be in the 1100 lb. range). You'll need 3/4" 16 ga. tubing as well, for the center tunnel etc. (not structural members).
The light weight issue is important in brakes, etc. as well. If you use brakes off a 2500 lb. car, you're going to have SERIOUS braking power, so there's no need to use, say, Lincoln Continental units - once you have enough power to lock up all four wheels easily, anything beyond that is wasted (and excess weight).
Have fun!