Corrosion, either of the chassis or bulkhead are the main things to watch for. Everything else can be dealt with relatively simply. Take a screwdriver or small hammer and have a poke around the chassis looking for holes, badly patched repairs etc. The bulkhead corners tend to rust and fall to bits.
Check the chassis numbers and documents match up with what you see. Because they're so easy to take apart, there are a few 'bitsa' Landys out there. Make sure what you're being sold is what is being advertised.
Ignore mileage and go on condition. With the variety of ways a Landy can be used, mileage isn't a particularly good indicator of whether it's good or not. I'd much rather have a high-mileage one that's been used as a car than a low-mileage one that's been bashed around a quarry all its life.
1980s Land Rovers (technically a Ninety or One-Ten, not a Defender) would have had either a 2.5L non-turbo diesel (up to 1986, and ex-military) or turbo diesel (1986-1990) 2.5L petrol or 3.5L V8 petrol. Some early 110s had the older 2.25L engines. The non-turbo diesels are fairly slow but very sturdy engines. If you're not in a particular hurry they're perfectly good. The Diesel Turbo got a bad reputation that isn't entirely deserved. Maintain it properly and it will give good service, and be a bit quicker than the non-turbo diesels. It's a bit of a gamble as to whether you get a good one though as it's easy to 'hide' a bad example that's been poorly maintained. The petrol engines are a bit quieter and give reasonable power, but can be thirsty.
The 1990s saw the Ninety and One-Ten rebranded as the Defender, and with it the introduction of the 200tdi and later the 300tdi direct injection diesels. These are generally better engines, and many have been retrofitted to older Ninety or One-Tens when knackered Discoverys with good engines were cheap. Theoretically the 2.5 petrol remained available until about 1995, but the majority of 1990s Defenders will be tdi-powered.
Expect to pay a bit more for a 200/300tdi, and to a lesser extent the 3.5 V8. If you don't cover particularly high mileages, a 2.5 petrol or non-turbo diesel might be a good option as these will be cheaper to buy.
From 1999 to 2006, Defenders were pretty much all fitted with the TD5 5-cylinder engine, and with it an updated dashboard. These will be more expensive again than the earlier tdi-powered models.
Ninetys tend to be more sought after than one-tens which can push prices up. Station wagon models with the side-facing rear seats are fine for short journeys, but not brilliant for long distances or carrying both passengers and stuff. If you regularly carry more than one passenger, a 110 might be a better option. With the rear benches removed you get plenty of space in the back, and room for 5/6 people.