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...
If you go with a 347 do a aftermarket block in case you want to add boost later. If you are dead set on a NA a 393 or 408 with a t56 Magnum behind it would be fun.
Falken Wildpeak AT3s are great all around. If you want a better winter tire pick up a set up used rims and put Ice Gaurds on them. You won't be disappointed .
https://www.ebay.com/itm/334109820328?mkevt=1&mkcid=1&mkrid=711-53200-19255-0&campid=5337259887&toolid=10001&customid=dd0c5ece22fb11eca90f32fabf77f97d0INT
hard to beat this deal
https://slickdeals.net/f/15207376-samsung-75-q8dt-4k-qled-tv-2020-w-allstate-protection-1999-99-at-costco?src=SiteSearchV2Algo1
spend a little more and be happy
I always top the tank with e85 and add stabil. I normally send the injectors in every 2-3 to be cleaned. Others will argue that it's not necessary but the before and after flow sheet shows the truth.