you need bmw LL01 approved oil. check the back of the bottle for that.
i am still under maintenance warranty for another year, but i do my own oil changes at 6 months.
i usually wait for a sale from my local autozone, advance auto parts, etc. stores. they will usually have 5 qts of oil and filter on sale for like $40.
it is usually mobil 1 full synthetic. i forget who makes the oil filter for our cars.
i get the mobil 1 0w40 because that is their european formula which is bmw ll01 approved. i end up buying it twice so i have the required seven qts of oil. the second set i buy, i buy an oil filter for my wife's car and get her regular oil and save the synthetic for my next oil change.