I own an RR fitted with a VM 2.5 turbo and from my experience the engine is likely to be the last of your problems as I have found mine to be very reliable, others may not agree with this of course.
It does not have the pulling power of the 300Tdi, especially below 2000 rpm when the turbo cuts in and it takes off like a rocket. I like to keep mine between 1500 and 2500 rpm with the ocasional excursion to 3000. My RR has completed 187K so is treated with respect.
Overheating
From what I have read this is likely to be a radiator or blocked hose problem. The bottom hose on the rad is a swine to get to and so they are not flushed as often as they should be.
MOT
You have not said why it does not have an MOT but if its anything like my RR it may be the inner wings, sills or body mounts that have rotted away.
Body & Chassis
On a Range Rover the body is in two layers. There is a steel inner structure on which all the external panels are attached. To check the body mounts you need to look under the vehicle and while you are about it lift the carpets as they can hide rotten floor panels.
All parts of the body can be repaired and parts are quite cheap but be prepared to spend a lot of time on it. If required the chassis can also be repaired but it all adds to the cost unless you can weld yourself.
VM Engine
Just briefly the majority of problems I have heard, not experienced, with this engine is overheating, heads cracking, and head casket failure. All of which are preventable. When I bought my RR in June 2005 I checked it over repaired two cracked heads and replaced the head and manifold caskets. I tightened the heads down as detailed in the Workshop manual and thus far its been OK. Its not a perfect engine but runs well.
Economy
I get 30 to 32 mpg on a run and 26-28 around the town.
As you a new to range Rovers it may pay you to get an experienced engineer to have a look at the vehicle for you, I relied on the workshop manual plus a few engineers who were prepared to help.
If you need any further information can you detail
a) Date on which the vehicle was registered.
b)the size of the VM engine, it will be a 2.4 or 2.5,
c) mileage
Best of luck
Mike