Graham, just to alert you: By asking for oil-recommendations you hit a wasp nest !
This is the top fierce discussed subject ever !
One party is convinced of using single grade mineral oil (e.g. SAE 40) without any additives (due to Steffen's explanation),
the other party uses cheap, multigrade DIY-Store mineral oil ( e.g. 15 W 40) and argues: If the motor was rebuilt and clean inside ( the centrifuge on the crankshaft),
and with frequent oil-changes as recommended by BMW, you don't have to worry about floating dirt.
Then again we have some guys, which use high-grade synthetic oils....
hard to give a general recommedation - it depends on each individual engine-status, environmental conditions and driving style.
For my own experience, I started with multigrade, cheap DIY 15-W40 in the eighties, after the motor was rebuilt, then switched over to single grade SAE W40.
But it bothered me to remove the oil-pan every 2 or 3 oil-services to clean the inside off, and also this "compressor-oil" is very sticky, like hot tar.
It was no fun adjusting the valve clearance with everything sticking.
Now i switched back to 10-W40 since the last oil-service.
You can also use this for the gearbox and rear-drive, it woun't do no harm. But some say a GL3-specification gear-oil is better and appropriate for the latter two applications. We will see what the following posts recommend.