This is a very common question and also a very good one.
The Discovery series one (DI) ran from 1989-1999, US models from 1994-1999.
Pre-1996 models have the 3.9L V8 with a distributor, all models after that have the 4.0L engine and electronic ignition.
There are thee trim levels and all had the 7 passenger option.
Common DI problems are as follows.
Sunroofs not working due to bad tracks.
Power windows not working due to a bad window regulator, easy fix.
Rear windows not working due to a cracked window lift ECU, easy fix.
Power door lock actuators not working, easy fix.
ABS light staying on, could be a bad wheel speed sensor or a bad ABS modulator. Could be expensive or free to fix.
Center Differential Lock (CDL) lever being seized due to lack of use.
Cargo door not opening from the out side, pop the LR emblem off and lube it with silicone spray.
The Discovery series II (DII) ran from 1999.5-2004.
The 2003 and 2004 model years have the 4.6L V8.
1999.5-early 2001 have the CDL as well as the 2004.
The DII also came in three trim levels and all had the 7 passenger option.
The 2003 has potential oil pump problems and the only fix is a new engine.
Common DII problems are as follows.
Power windows not working due to bad window regulators, easy fix.
Power door locks not working due to bad lock actuators, easy fix.
The cranks shaft sensor (CKS) going bad.
The throttle body heater plate leaking, easy fix.
Head gaskets going bad, change your coolant every 2 years and you can help avoid this.
The front driveshaft MUST be rebuilt using greasable u-joints, if you dont you WILL be buying a new transmission. ($7,000)
The "3 amigos", that is the Hill Decent Control (HDC), ABS and Traction Control (TC) lights all being on at the same time.
The Self Leveling Suspension (SLS) going flat.
The Secondary Air Injection (SAI) pump can be noisy, clean the air filter to it every 6 months.
The Active Cornering Enhancement (ACE) is very reliable and a good option.
All model years require premium gas, you can expect 12-14 MPG in the city and 16-18 MPG on the expressway.
is a good used parts supplier.
is a great new parts supplier.
Go to AtlanticBritish and find the "tech tips" page and read up on them, print the pages that pertain to you, like "how to reset the HVAC from C* to F*"
Do your research.
Test drive many, dont buy the first one that you come across.