I agree with Hippo!
Take someone else that knows SOMETHING about cars, and ideally Landrovers.
I think about the stuff I missed when buying my Disco, and it's criminal really. I find myself trying to look at everything, knowing it was REALLY cheap, so not wanting to lose it. I've since of course realised ALL teh things that are wrong with it would have given me another £3-400 to spend on a different one...
I don't know about TDi's, but I imagine start it from Cold. (Ask them not to start it beforehand). Check for blue/black smoke, which should clear up when it's warm. (Somebody please feel free to correct me if I'm talking tosh here)
Run it. Stop it. Wait a full 5 minutes before trying to start it again. (I've had several cars that will start again immediately, but give it 5 minutes, and it won't start for love nor money for a while longer).
Check Low/Hi/Difflock, and any crunch on Syncro going up and down the gears.
Rust. Check the bulkhead - bottom and top of the A-Pillar. If the rear crossmember has started to go, and/or the outriggers be prepared for a LOT of welding. Nothing IMO is too bad, as they come to bits like Meccano, but it does take time, garage space, and a little bit of bravery to tear your new toy to component parts!
Paint job. Last 90 I bought was hand painted. I thought I could live with it - but it was bad, and would have cost a fortune to put right.
Check the MOT history!! Dead easy if you know the registration.
https://www.check-mot.service.gov.uk/?_ga=2.129639628.1127656469.1551386914-666549656.1525368916
Use a free 'HPI' type checking site before you even go. I knew my Disco was stolen/recovered before the seller did, which helped with price negotiation.!
Enjoy it - don't pay over the odds, and be prepared to walk away if you don't like something. There WILL be more out there somewhere, usually about 2 days after you've bought something.....