First off – good luck with your potential 65 Continental purchase!
For oil I’ve had excellent luck using Shell Rotella T diesel spec oil in all my vehicles past and present. Even though some of the zinc was removed from it a few years ago as required by the new regulations it still has more in it than most other oils.
For oil additives I’ve been using Lucas Oil Stabilizer, and I also use their fuel stabilizer fairly frequently. I also like to run a can of Sea Foam additive through the fuel system every so often to keep things clear.
Ethanol fuels can cause problems with older vehicle fuel systems. The alcohol breaks down the rubber bits a lot quicker than plain old gasoline. I’d suggest replacing all the rubber lines with PTFE lined hose. Gates Barricade fuel hose will work as well. Carburetors can be affected too, but most rebuild kits out there are compatible with newer fuels.
As for other pitfalls there are some things to be aware of, such as factory timing chain set replacements. The original cam gear is nylon coated and will degrade and fall apart eventually, even on a low mileage car. Bits and pieces of the gear wind up in the oil pan and can work their way into the oil pump among other places. I’ve experienced this firsthand on a 65 Continental I owned years ago.
There are some other potential issues, but generally they’re the same as most other vintage cars – worn valve guides, worn and/or damaged valve stem seals, weak valve springs, sloppy valve guides to name a few potential engine issues you may run across. If the car has been maintained these shouldn’t be much of an issue.
Resistance is Futile.