I would love to tell you how bad those Jaguars and that Bimmer would be on your budget but I have the feeling insurance will chase you away soon enough. Older 7ers are reliable to a point, but they are nowhere near as nice as the newer models.
I recommend you read up here and see what I mean;
http://e38.org/
So now;
The most common problem will be the radiators and the catalytic converters going bad. BMW will charge around $2500 to fix all of it, you can do it on your own or privately for $1000-1500 installed.
Make sure all the pixels in the cars headunit display, navigation and all readouts. These parts are prone to going bad. This is especially important on some 98's 99's and all last year models thereafter because they either had regular navigation, widescreen nav, or phone packages as standard or dealer standard options.
Some dealers will fix this out of goodwill,
some specific cars had specific warranties that cover this, and most will suffer from it. Otherwise expect to pay about $300-500 each for two modules that will need to be replaced if they were not already.
Please dear god make sure every single electrical function on the car is tested beforehand. My dad used to have the 750il and all the windows and the sunroof decided they wanted to voodoo dance on me during a horrible rainstorm. The dealer said they could not replicate the problem but after some checking with some forums I found the window regulators like to go bad. Not an expensive fix but these will go bad, so get them checked. Small $10 and $20 electrical components are scattered everywhere, if they fail it will drive you crazy chasing the problems.
Other than that 98+ models are pretty solid and probably still on extended or qualify for a CPO extension. Our car was a v12 and it cost only about $1500 in maintenance a year, by contrast the LS400 was a little more than half that cost. Lexus does not have as comprehensive a service contract as BMW offers, in terms of parts warranties and repairs coverage the two are about even.
Like I said here;
http://supraforums.com/forum/showthread.php?t=425939
Your transmission
could go bad, and it will be 100% an owner of the car's fault. Make sure the car was cared for correctly. Otherwise this is a $4500 repair, it is not a known problem in 7ers like it is in 3ers but it's the same lax attitude that leads to the same problems.
You will also hear alot of crap about Nikasil v8's and BMW engines failing because these Nikasil coated internals are eating themselves up. Again, this is due to the treatment of the cars. Porsche also used Nikasil but didn't have a bad reputation for it only because the owners are proactive about taking care of the engine the way it was meant to be used.
If you have 15k for a car and can come up with maybe 4k a year for insurance and another 2-3k for standard scheduled maintenance, go for it. Not much goes wrong on the v8 cars as most of them are well taken care of.
Spend 20-25k initially but with only yearly work at around 1-2k, instead of 15k with 2-3k maintenance fees; and you won't have any serious problems like a Mercedes.
P.S. The cup holders are not worth shit. Rip them out and mail them back to Munich. :hay: