Welcome to the Team Chris!
I am not a big fan of synthetic oils (all oils are synthetic: that is they are refined, it is only a matter of degree). I feel the extra cost isn't worth the perceived benefit. Especially in an older small block Chevy that has primitive oil control (your might even have a piece of rope as an oil seal) and has known issues with oil leaks even with thicker with dead dinosaur oil. Synthetics will pour out like water if you have any leaks now. A better choice is Valvoline High mileage motor oil and a can of GM EOS or Lucas ZDDP oil supplement.
Todays synthetic motor oils have approximately 600 ppm ZDDP with oils like Valvoline High Mileage having 880 ppm ZDDP. This is down from SAE 30 SE/CC motor oil you would have bought back in 1970 which had 1400 ppm of ZDDP. ZDDP has been falling since 1975 when the first catalytic converter was installed on autos. Racing oil has 1100 ppm ZDDP but they have no detergents needed to buffer the acids and trap the blow by contaminates from normal driving (you change racing oil after every race not at 3000 miles)
As to your gas tank: gas turns to varnish with time. It is how the ancient Greeks found varnish to paint their statues and bas reliefs on their temples from oil seeps where the gas had turned to varnish from aging. The Oracle of Delphi got high sniffing gasoline fumes as there is a petroleum weep were oil springs out of the ground along with volcanic gasses that are equally poisonous and hallucinogenic. Varnish is great for painting wood and porous stone but bad for carburetors.
The fuel system will have to be cleaned by dropping the tank and flushing the lines with brake cleaner. If there is gas in the carb it will have to be rebuilt, or buy one already rebuilt if you are not worried about the car not retaining it's numbers matching aspect.