For an M52 328i I run a full-synthetic oil meeting BMW Longlife-01 (LL-01) / ACEA A3/B4. 5W-40 is the safe all-round grade for most climates; BMW's period chart also allows 5W-30 and 10W-40 by temperature.
How much: the M50/M52 six takes about 6.5 litres with a filter change. I always finish to the dipstick rather than trusting the quoted number.
How often: every 5,000 to 7,500 miles or once a year. These engines last far better on that than on BMW's stretched Longlife interval.
For reference, the other E36 engines: the M42/M44 four takes about 4.0 to 4.5 litres, and the S50/S52 M3 about 6.0 to 6.5 litres. M3 owners often run 10W-60 for hard track use; that is an enthusiast call for sustained high oil temperatures, not the baseline.
And do not confuse this with gearbox fluid: the manual and the automatic take ATF/MTF, the engine takes the oil above.
For the change you want an LL-01 5W-40 full-synthetic and an oil filter.