The mechanic gave me some random brand with 5W-40. Suspicious, i looked it up and this is what i remember. As far as i understand, you want to use a full synthetic with little or no additives (which is the BMW list). I think they also have a list of "longlife" approved oils.
The viscosity(thickness) of the oil depends on the temperature. You basically want to pick something that wont be too thick when its cold and wont be too thin when its hot. The format is like #W-##
The first part (#W) is the rating for cold (Viscosity at 0 degrees C). 0W thinner & 10W thicker. => Colder weather (like freezing and snow) use 0W and hotter weather use 10W
The second part (##) is the rating for heat (viscsity at 100 degrees C). 30 is thinner & 40 is thicker. => Colder weather use 30W and hotter weather use 40W
Ive been told (so its not a fact, but just what ive heard) that thicker oil is also better for higher mileage cars. Since the seals are starting to wear out, the thicker oil tends to leak less (through the seals) and you will burn less oil.