I've been quoted already and wasn't even here
I just had a talk about Discos with another friend today. Let's get one thing straight: they are not well thought out reliable cars. They are the anti-Toyota. Odd ergonomics, highly variable build quality, overly complex designs, and soul just pouring out like a british car leaking oil...wait...
But still, I love mine. It does exactly what I need it to do, and has some of the je ne sais quois that someone who's first car was a 35 year old MG requires. It is tough as nails, holds tons of people and crap inside, drives nicely, has lots of comfort and goodies and stuff, was cheap to buy and insure, has a great enthusiast community, and lots of good used part availability, will drive through 3' of water, and climb a greased flagpole.
Mine is a 99 Disco Series II SE7 (top trim level, 7 passenger). Nearly 151k miles and going strong. I've owned it for more than a year and a half, put 20k miles on it (sometimes a daily driver, sometimes it sits for months, sometimes I beat the hell out of it towing my 4500# boat). I've only had to do maintenance to it: tune up, battery, belt, fluid changes, and an A/C hose, and I don't see anything upcoming that is going to need any work.
The DiscoIIs are a much nicer car and daily driver, and more reliable than the D1s, and about 98% as good off road. From 99-mid 2001 there was still a center differential lock in the transfer case but no lever in the cockpit to engage it, but that can be added easily. They removed the CDL for late 01s, 02s and 03s, and put it back for the 04s. Major mechanicals are all fairly reliable, it's just the little stuff like sensors and crap that goes. Engine electronics are all Bosch, trans is ZF, etc.
At your price point, look at late 99s and 2000 models. There is no simple list of things to look for to be broken, as it could be nearly anything. Try to find a car that has been good and reliable and been maintained for it's whole life. I looked for a while for mine, it was a 2 enthusiast owner car that had never had any real problems, and had had plenty of preventative maintenance. Find a car with no dash lights on (the 3 amigos plague many a DII), and that has had it's front driveshaft replaced (non serviceable part, and when the U joint breaks, the driveshaft bitch slaps the transmission).
I have a hard time recommending one to someone, as they can be really hit or miss depending on how drunk the limeys putting it together were that day, but I really like mine and think you might be the right kind of crazy to enjoy one. The best online resource for them is DiscoWeb. Lots of info over there, and they won't blow smoke up your ass like most model specific boards, they fully acknowledge the pros and cons of these things, and choose to put up with the "personality" as they like the rest of it.