While the brand doesn't really matter, as mentioned above, the certifications and specifications of the oil do matter. Many oil companies make products that meet the required specs.

You want an API SM or SN oil, as those are the most recent specs. Your owner's manual will reference an earlier API oil like an SJ, but they are backwards compatible, so take advantage of the new oils. Some of us feel that it is important that it actually be certified to the API standard; others claim that it doesn't matter. Your call. The API certified oils have an API mark on the bottle.

You want a 5w-30, or a 5w-40. That is the weight of the oil, and it matters as well.

You specifically do not want an oil that claims to be BMW LL-04. This was a BMW long life spec from 2004 that BMW later pulled back on for North American gasoline fueled vehicles, as this spec oil turned out to not stand up to the fuels we typically have in North America, so it didn't last as long. Some oils that are formulated for European vehicles use this spec, but it is a negative and not a positive for a gasoline fueled vehicle in North America. If you want a BMW Long Life (LL) spec, you can use LL-01, but it is 13 years out of date so it is up to you whether you worry about it or not. Many of us don't, as there has been a lot of progress in oil formulations in the last decade.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue