Brian, Welcome to the Forum! Is the '35 a driver now, or has it sat for some time? It may have already been retro'd for the corn gas, but good to be aware of those possible issues anyway. You can pull the fuel sender and take pics with your cel phone to get an idea of what's happening there, and to check the condition of youer sender. You should know that the fuel line itself can develop issues from the corn gas, and is replaceable with new as original from some suppliers. The flex line is replaceable with a new alcohol resistant one also, see the ad in the V8 Times. Pump diaphragm should also be checked, as well as gaskets on pump and carb. Pump valves and carb needles are vulnerable if not the resistant type. A fuel filter is good to place near the tank, and many also install an electric pump to help with fuel issues.
Engine oil should be multi-grade of a good quality, 10-30 is the usual choice. Some use synthetic oil, most use dinosaur oil. All should be detergent regardless. If you have a filter, it does help some, even though it is a bypass system, all oil passes through the filter within 15~20 miles. Filters also help in keeping temperatures down. Change oil and filter about 3~4k miles, do your own lube jobs or personally direct those that do, as the kids don't even know what a zerk is these days.