For older Minis, 20w-50 is generally preferred.
As Larry says, the engine doesn't really need that heavy an oil, but the transmission does....and since the transmission runs in the oil sump, 20w-50 works well. I use Castrol, but any quality oil will do.
Here in the Great White North, the heavier oil isn't a problem, since most of us put our Minis into hibernation during the winter (too much salt on the roads).
Synthetics are fine for the engine, but I'm not sure how good they'd be for the transmission.