Here's my second one, and my daily driver for the past year and a half:
2001 (last year) 740i Sport. 165k miles on it now. At 143k it got it's timing chain guides done, as well as teh valley pan gasket and cooling system gone through.
Timing chain guides could go bad at any point after about 120k miles, but my previous one was on it's original TCGs at 185k miles. VANOS is only on the '99-01s (M62TU engine) which are easily discerned by being the facelift cars (scooped headlights) so pre facelift ('95-98) don't have it. The '95s have the 4.0 liter V8 that had nikasil problems in the early days, but any that are still driving are either replacement engines or will never have the problem (no sulfur content in modern fuels to eat away at the liners).
As was mentioned, the V12 cars have fewer problems overall than the V8 cars, due to no TCGs, no VANOs, no OSV problems, and a more robust cooling system (though the radiators and expansion tanks can still crack due to the plastic tanks just like the V8 cars. Luckily they are cheap)
The most desirable ones are the '99-01 740i Sports, due to the added performance goodies (lowered springs, different shocks, 3.15:1 final drive, steptronic trans with manual mode and high stall converter) and cosmetic stuff (M parallel wheels, shadowline trim (blacked out), Vavona redwood interior trim, Sport seats with adjustable thigh support and more aggressive bolstering). The 740iL Sports did not get the performance goodies, only the cosmetic ones.
The iLs are the ones to have if you are carrying back seat passengers, and the 750 is the ultimate for that, with power reclining heated rear seats.
Here's my old 740iL:
Neither of my cars have had pixel issues, but it is a common thing (easily fixed these days, either DIY or though vendors). There's a huge community of owners, including my own Midatlantic 7s. E38.org is the best source of info on them. Any questions, don't hesitate to ask me, as I've been involved in the E38 community since 2006.
Oh, last thin... KBB excellent condition private party price is a mere $4500. BUT, do not buy one on price. Spend a bit more for an enthusiast owned one with records. Both of mine were $7500 cars and were bargains at that price. The '01 Sports can sell in good condition from $7500-15,000. Spend a bit more than the bare minimum and you will get a car that treats you well. Don't worry so much about mileage as condition. My first one cost me $1500 in repairs and maintenance over a 5 year span, and my current one, that I've had for a year and a half, has cost me $102 in repairs (braided stainless steel brake hoses and an instrument cluster bulb) and $660 in maintenance (new set of Sumitomo tires, a set of Akibono Euro ceramic pads, and an oil change). Shouldn't need tires or pads for another 3-5 years, so it should be pretty cheap overall to own.