I am far from being a C3 Expert
I always check the fender seams to see if it is still factory seams or had topsourround or panels replaced. Then see that the body lines are correct and everythhing works without binding, e.g. Hood, Doors, Windows and turn the steering wheel from stop to stop and check tire clearance both infront and inback of the tire.
Check back compartment to see if it is intact and solid, esp. the battery compartment. Check all rubber bushings front and rear suspension, as well the shocks, springs and brake lines. I also jackup the rear and do a cursory check of the bearings and half/shafts, also ask about trailing arms, when or have they been rebuilt or replaced, and who did the work.. not something done by a novice
If I get serious then I pull one front and one back tire and check the disc brakes for wear and how the park brake works. I also take a tape measure and measure from the top of each fender well to the ground to get a ball park idea how level or if leveling the car is possible, with in 3/8" or so isn't too bad (from side to side).
Look for water stains, and take a phillips screwdriver and check a few of the screws in the T-Top frame make sure they unscrew and tighten up, same with the door panel.
Then drive it, here I get it up to cruising speed 65 ~ 85 somewhere then let off the gas until engine slow the car down to around 40 ~ 45 then punch it and see if it smokes any and if the carb works right.
Sitting in the driveway, push the clutch in and go to reverse (staight from neutral) if the clutch is good and adjusted it should slide right in to reverse, you shouldn't have to go to 1st or 2nd before going to reverse to keep it from grinding
Rust... the frame, use the phillips screw driver to poke a few spots, then check the birdcage, Some folks use a business card and slip it between the frame and the chome covers, IF you are serious about buying it, I recommend taking the panels off and checking, also another place to remove the sidekick panels and use a flash light to see if there is rust streaks on the frame and inside panel up toward the windshield..
Then trust your gut or get a mech to to check it out..
Somewhere here at CAC is a check list when looking to purchase a Corvette, might be in the Tech Center ..

I'm sure with your computer skills and talent you can find it

if not let me know and I go take a look
Good luck on the 73 and if you get it for $9,500 or within a couple thousand bucks, I'd be shocked :eek
Bud