Good bike goes basket
I wouldn't worry about the chain yet. Pull the oil pan and see how much goo is in there and read it like a gypsy reads tea leaves. If the sludge is minimal, I would leave as much as is as possible. Since the jugs are off and pistons out I would measure the ring gaps, if in spec, a quick hone and back together. Big end shells would probably be a good "While I'm in there" but you will need to purchase new bolts and a 12pt male wrench to do this. If there is no in and out play then they are probably good, there is always a bit of deceptive side-to-side play.
If you cannot help yourself check out the heads. With heads off, inspect the mating surfaces of the head-to-barrel for head gasket failure, I'd personally renew, but the existing may be just fine.
Look at the exhaust valves for recession in the head. If the valves are still "proud" in the head leave them alone. If it makes you feel better, remove the valves and inspect seats and edges. You may want to lap them in to clean up a bit.
Don't get too deep too fast. Be patient and diligent. The torque wrench is your friend and the BMW engineers knew what they were doing, follow directions.
After it is back together and running, time it with a strobe light. A bouncy timing mark at idle is a sign of a loose timing chain or a sloppy advance mechanism. The chain will most likely be noisy if it is an issue.
Never underestimate the laxative properties of motorcycling.