After the warranty ends the prices DROP! DIY is a must unless you have deep pockets. If you like keeping the car in good shape as a DD it can still nickel and dime you to insanity even without the big issues.
Since you specified you are looking at the 4.4L V8's, big problems are the timing chain guides and downgraded transmission. Timing chain guides are plastic coated and have been known to break apart between 125k-275k miles but at this point age may be as big a factor as mileage. Removing the timing covers to inspect the guides is quite a job so usually people just drop the oil pan and check for plastic pieces sitting in it. A good maintenance item to help preserve them is to change the tensioner ($100 & 15 minutes). As for the transmission the best thing to do is go for a long test drive from a COLD start and pay close attention to every shift. It seems when they went to a bigger engine they also went to a smaller trans, along with saying it had "Lifetime Fluid"! A fluid (gravity drain & refill) and filter change should be high on your maintenance list.
Nickel and dime stuff: window regulators, cup holders, radio/NAV, cluster or MID pixels, heater control valves, FSR/blower motor, ignition switch, driver seat control module, fuel pump.
Around 100k there is a good chance those cars will be due for tires, brakes & suspension (EDC is $$$$).
Before a test drive check every button/switch/light/option to its full extent (ex. each window fully down & up). Speaking of lights, with the key turned but engine off make sure all the warning lights work on the cluster. If you find one you like take it to someone very familiar with 15-20yo BMW's for a PPI, usually a dealership is great for this but ask around for your area. A stack of receipts/records is always nice to see from the sellor also.
Sent from the future using the app downloaded to my neural implant.