Whatever you do, don't try to break it in on synthetic oil. I would go until at least you second or third oil change before using synthetic. No one has mentioned Schaeffers oil yet, and while they do not make a synthetic 10W-40, they do make an excellent full-syn 5W-40 and a 15W-40 blend. Either of these would be a low-wearing, clean running SAE 40 oil for your BMW. See the site sponsor for Schaeffers here or you could try to find it locally, which can be iffy.
That reminds me, I never did send any Schaeffers to Sunruh for his torture-testing. Next time I order some, I will send a few quarts if he is still up to testing.