Typically you can start up the car cold / no pressure on the cooling system with the radiator cap off if a headgasket is bad bubbles will be seen in the coolant. For really small leaks you can use a combustion gas tester for the coolant.
Based on the above it sounds like you have a air bubble...
If the car is not up to your standards without paint work, I would walk. Increase your budget and find a cleaner car. Out of interest call a local body shop with a good reputation and ask what a ball park number on a complete paint job. Including door jams, hood and trunk lids and everything...
A si trim on a someday 347 would be less then ideal. I ran a D1 on a stock block motor for 3 seasons before I upgraded to a R block 347. 80 lb frs injectors , blow through maf , ran e50-e70. Never lost a headgasket. Do some research and plan it so the parts transfer to future engine combo...