That engine was built back in the day when Mult-Grade oils were just being figured out. Any owners manual for that engine will specify straight SAE 30 HD and a few multi's.
The issue with all conventional multi-grades is they start with the W rating oil and add Viscosity Index Improvers (VII's) to get to the higher number (like XW-30), so as they shear down, they become 20's, etc. VII's are not oil. They are form of plastic. They carry oil in the chain structure, but they are not oil. SAE XX HD is all oil and is good for old seals and gaskets, plus it does really well for engines that sit a lot between start-ups.
And any real synthetic will not be terribly friendly to the old dried out and hard cork gaskets used back then. So you MAY get a few more leaks and weeps ...
So, gotta ask the questions. How do you intend to operate this engine. Only mild days and cruising? Or full time all seasons including cold snowy winters? Trips to the drag strip? How many miles on the engine? Any rough running, knocks, ticks, etc?
If it's a mild weather cruiser - SAE 30 HD in your favorite brand. If trips to the drag strip and mild weather SAE 40 HD. If year round including cold weather, prolly a 15W-40 HDEO like Chevron Delo 400 LE.
If it's a true 1968 engine, prolly a 327, I'd be taking it sort of easy on it. You don't know what condition the timing chain is in ... If it's the OEM unit, it's almost guaranteed that it's stretched and crusty, almost running dry and not happy ...
The way to make these engines (all SBC's) really happy is to replace the timing chain and the sprockets with a good solid unit from a reputable source. You can do a timing chain w/o dropping the pan. It does not need to be a roller chain, but that would not hurt. While you are in there, you drill the lifter gallery end plugs 0.030" and let them dribble oil on the cam sprocket continuously. The chain stays wet, and all is good.
If you are struggling with oil pressure, only drill one side. New timing cover gaskets, new front seal, and it's all good. Once you have a new chain, the timing will be much better, so the engine will act more like the original. Then you can decide if you want to start chasing other leaks, weeps, the RMS, etc.