The first requirement is to ensure you have the adequate ZDDP levels this means 1200 ppm or higher based on the the current data out there from lube manufacturers. This can be had by either buying the numerous racing oils available on the market suited for the flat tappet motors or using an off the shelf
oil with less than 1200 ppm (nowadays I think 500-800 ppm is more common on the published data sheets) and then add the ZDDP containing
oil additives on the market (include some the cam break-in
oil additives). Now regarding the viscosity question for your climate in CA assuming this is street driven and does not spend time racing at high rpm, oils in the 10-30 and 10-40 range or even 15-40 (Shell Rotella-T) will be fine. These days, the engine oil technology in even the cheapest no-name SAE spec oils are light years ahead of where we were when the these V8s were made. The 15W-50 mobil 1 ref, is a
synthetic and is claimed to have ZDDP in the 1300/1400 ppm range and would also work.
Synthetic is really not necessary unless you race and your oil temps sit north of 240F. Selection could also depend on the bottom end build and clearances being used etc etc. But assuming nothing unique regarding bearing clearances above still applies.