You can still purchase straight grade oils as well. You should be ok running a modern oil with a similar base viscosity, a 10W-40 will have the viscosity of a 10W oil and has additives to offer the protection of a 40W oil when warm.
I would not suggest a synthetic, my experience and some ancedotes revolve around it allowing an engine that did not have an noticeable oil use to begin consuming far more oil on those expensive synthetics. Some brands behave better, some are not so great. I didn't care for the recommended synthetic ATF in my T56 manual, it seemed to stick on shifts much more after only a few hundred miles, problem went away after switching back. If I were to purchase a Z06 or some other car that came recommended to use Mobil One, I would to avoid warranty issues with potential deposits or lack of film protection under hard use, but would also assume that the engine was engineered and tested for proper operation with that oil.
The gasoline is another story, 50 years is right around the time of leaded gas additives and many motors from even the late 60s need the addition of hardened valve seats in order to not allow the valves to damage the valve seats. The more a high performance motor with high compression and especially aluminum cylinder heads, the more likely you'll want to research what fuels and/or additives are safe. You can still purchase the leaded fuel for off-road use and marine use, no idea where though.
You can find a ton more info with a google search of something like "leaded fuel replacement"
The manner of operation matters too, if you're just out for a Sunday cruise its not going to be as hard on anything as a race around a road course with lots of wide open throttle.
For curiousity, what car engine? An old Fireball 8 or a Stude or what?
