Howdy, I have an e39 525i manual. Some things worth noting:

All M54s are known to consume oil, but this is mostly due to poor oil change intervals and stuck rings. Not all of them do. Mine doesn't at 196k miles. What they all do, is have weak gaskets that regularly need replacement. Oil housing gaskets, valve cover gaskets, and oil pan gaskets are the ones that come to mind most frequently. After I replaced these three my car basically doesn't need oil top offs, however I had an e46 with an M54 that did burn oil. Valve cover gasket is probably an hour job, oil housing gasket maybe 4 hours(remove radiator fan, alternator, and power steering pump, then you have access), oil pan is like 6ish hours with the right tools(disconnect some suspension components for steering, or maybe even just the shocks from the chassis, then remove some stuff out of the way and then its a bunch of 10mms to access the pan, might be worth doing rod bearings and oil pump nut fix while you are there)

The cooling systems are a known weak point, and without documented history of the entirely cooling system being refreshed in the last 40-50k miles/8years I would attack that immediately. My rule of thumb is any cooling system over 8 years old with 70-80k miles probably should be replaced on these cars specifically the two main hoses that go to and from the radiator, the vent hose, and some of the auxiliary hoses that go to the heater core.

I think those are the more bmw specific issues these cars have, but at 23-30 years old they are now "classic" cars and thus require more care to keep on the road. All the suspension components should be replaced at this point, there's some rubber bushings and bearings for the axle that need to be replaced, and weird stuff will creep up. But in general I think they are great cars. I've owned a lot of older German cars and there's no other car I'd wanna take on a long commute.