Let's see, PP, Castrol Syntec are a couple that come to mind. Synthetic is required for long (manufacturer recommended) oil changes. Conventional will be fine for 3-4k miles with Auto-rx. I put 18oz. ARX in with 10W-40 Quaker State in a 98 740i with 102k miles a few days ago. They will bring the car back to me at 105k, and I will put in 2 gallons Rotella 15W-40 and a new filter and send them out for another 3-4k miles. Their M62 engine does better with a XW-40 in it overall. For your engine, you could get mostly Castrol Syntec 5W-30 and mix in a quart or two of 10W-40 or just get some Syntec 5W-40 if you want to stay with one grade. I say 3-4k miles on synthetic is a waste and would run the ARX at least 5000 miles (just me) with synthetic group III synthetic oil. Same with the rinse and group III syn oil. Rotella synthetic 5W-40 is a group III synthetic and would work as well during clean or rinse with ARX, esp in hot weather.
If you don't want to spend a lot of money on oil during your rinse and clean, just get 5 quarts 5W-30, and 2 quarts of 10W-40 conventional Castrol GTX which is known to work well with ARX chemistry. If in the summer, perhaps use 10W-30 and a couple quarts of 10W-40. This mix will give you the higher viscosity SAE 30 at operating temp that works well in these engines for a 3000 mile interval while working with Auto-Rx. Simple and safe. Done it several times with great results.
