Because of the lower valve spring pressures inherent in a valve-in-block engine, cam wear (and therefore zinc content) is not nearly as important as in OHV engines. Any currently available conventional oil that meets later specifications will work fine. I would personally avoid synthetic oil for potential leakage and cost reasons. Also, no matter what that old guy down the block says, don't use non-detergent oil.
If the engine has been rebuilt properly, you can also save a few bucks by not using the heavier viscosity diesel oil. 10-30 automotive oil is fine; anything heavier just makes the oil pump work harder than it has to. Those guys with the PHD's that work for the oil companies formulate different additive packages for compression ignition and spark ignition engines for a reason.