My policy has always been to regard the oil in the engine after a rebuild as "sacrificial" I usually change it after 50 - 100 kilometers. After that I do a clearance, timing and balance check, I repeat the checks but the 2nd lot to f I up stays in for 3,000km or 6 months - whichever comes first.
After that the service interval is 3,500km or 12 months, whichever comes first.
Oil filter is changed every oil change.
I use Penrite HPR30 (20W-60). A mineral oil.
There is no reason whatsoever to put synthetic oil in an airhead. They are not designed for synthetics and may delay you lavishing such oil on them by developing leaks.
Of far, far greater concern is the fact that many synthetic oils contain little to bugger-all of an additive package called ZDDP (zinc). Modern engines designed for synthetic oil do not need Zinc so the manufacturers leave it out.
Zinc is essential for flat tappet engines like our Airheads. I do not wish to alarm you but there are zero, Nada and zip, new R45/65 cam followers available in the world right now. As these are the very part that breaks up in the absence of ZDDP I would look after the ones you have as they may never be more.
BMW heritage parts have 6,000 nice brand new, correctly chill cast followers for the long stroke engines in stock, unfortunately the guy who ran the business that used to finish grind them and then harden them, has retired.
Unless someone else steps up to make more cam followers for the R45/65 engine then what is available on the 2nd market is it. It is generally considered unwise to reuse a cam follower unless it is going. ACL into the engine it was fitted the - in the same position.
So, mineral oil with lots of ZDDP. In Oz that means basically Penrite or Nylon racing oil (which does have a lot more ZDDP than Penrite, but I distrust Nylon and regard them as the "Demtel" of oil blenders due to involvement in questionable products like tank additive injector cleaner and really crap oils aimed at supermarket sales.
There are some who dick about adding ZDDP to other oils like Shell Rotella. Rotella is a great oil and is amazingly cheap in large quantities, but it is a diesel oil and has detergent packs that I worry about suitability in a petrol engine.