Ian,
The engine in my 1993 Vitesse is the Rover T16 2 Litre Turbo @ 180BHP, and just over a year after mine they stopped putting Mahle forged pistons in the engines and using Rover ones, they sold the Vitesse Sport from 1994 I think onwards running @ 200BHP and this later became the standard Vitesse (1996).
Also in the Coupe you can find the standard 2 Litre T16, 2.7L V6(Honda) and also the 2.5L V6(Rover).
If you go for a 2 Litre Rover engine try for a 1993 one, but finding one will be hard as they were rare and new, but as long as you're not going to be running at any mad turbo boosts the later ones will be fine, you could always fit new pistons.
I've found the engine reliable but you must change fluids at stated intervals or you'll suffer head gasket failure. I use Mobil 1 0w/40 Fully Synthetic oil, DOT 5.1 brake fluid and change antifreeze every 2 years is a good idea. So far the CAS sensor has been replaced (Part cost £18 from Partsco) and the pipe from the manifold to the MAP sensor (£6, halfords). Fitted the car with a new slave cylinder seal this year and a new clutch, expect clutches to last 90,000 - 120,000 miles as long as you're sensible. The gearbox (PG1) is fine for the standard Vitesse but a little weak for the Vitesse sport but driven sensibly and changing the fluid for Rover MTF 94 every 2 years and it'll last, mine is still smooth and has minimum bearing whine which only recently appeared. The car is best run on 97 RON Super unleaded, i use optimax (98RON), otherwise the Rover MEMs computer will retard the timing to prevent engine knock.
If you keep on top of a Vitesse configured car it'll be fine, a service history is not essential as you can tell when someone's not looked after it. My colour is Flame Red and is one of the few 10 year old cars coloured red on the road which is actually still Red, annual or twice annual waxing is the trick. The Recaro seats keep you in place well and are comfortable, full leather seats aren't for racing around in as you could end up sliding about.
The Vitesse Sport has a Limited Slip Differential, my car is not equipped with one and I'm happy without but it would be a bonus just in case of an unexpected situation in the wet someday. I've found the brakes to be more than adequate but poor quality pads will produce alot of dust and mar the alloys. Vitesse sport has 17" 6 spoke alloys whereas standard Vitesse 16" 7 spoke. I use Michelin Sport 205/55 R16 tyres and they fair well.
If you got for a Sterling / V6 equipped Coupe then the 2.5 Litre would, on paper, be the best option. These engines were introduced towards the end of production and are every bit as fast/powerful as the 2.7 Litre Honda that'd been used since the 80's, but with better fuel consumption. There were alot of problems with these engines in the 800 when first introduced but are now sorted in the new 75's, there were alot of engine replacements under warranty from Rover.
The 2.7 Litre V6 is a good engine, will last forever but begins to sound tappity if not well looked after with oil changes.
As with any car Cambelt changes are important, every 30,000 is best for the T16 and although rover once specified 96,000 for the 2.7L V6, every 50,000 is more wise. You can probably persuade a garage to throw in a Cambelt change when you buy the car.
Check the ABS system is in working order and the bulb hasn't been disconnected by a dishonest garage. The gearbox in the V6's and the auto boxes are fine but look out for ones where fluid hasn't been changed, a burnt smell and black automatic transmission fluid means just don't bother.
The Pre-96 relaunch cars commonly have a much harsher ride, mine exhibits this so if you buy an early one you can always change the suspension for later parts at another date, but the sports models have hard suspension anyway so if you can give a little comfort for performance that's up to you.
I can't think of what else to put to looks out for, obviously check all electrical systems work and the key fob is included. The VID plate is located bottom right of passenger side door frame.
On a test drive let the car warm up first (rover say don't drive above 3,000 RPM until running temperature) and proceed to take the car through the gears with plenty revs, a faulty CAS sensor will read wild revs and cause fuel cut off when accelerating hard above 3,000 RPM in the turbo engined car and a faulty MAP sensor the same without the wild rev reading.
Faulty speedos can be fixed cheaply with part from a scrap yard, but mine's been fine so far.
I'd say 820 i/Si/SLi - Basic, best fuel consumption. 820 Vitesse (Turbo) - Speed (Vitesse is french for speed!), better fuel consumption than the V6. 825/827 i/Si/SLi/Sterling - Luxury (V6 engined) but you pay for power with fuel consumption. 825D - I don't think you'll find a Coupe with the 2.5L Diesel engine, but it's a good engine not heard complaints.
The joys of owning are simply a comfortable luxury car that doesn't cost too much anymore, you feel safe and the sporty models really can be, but remember the car is 16ft long and don't expect to be able to corner like you're in a peueot 205. The Vitesse / Vitesse sport really have kick once you're on boost. Conflicting data is common but i find from reliable sources the 820 takes just over 10 seconds 0-60, the Vitesse 7.8, Vitesse Sport just over 7 (7.1 - 7.3), the 2.7L V6 7.9s, 2.5D near 11s and the 2.5 V6 is around the same as the 2.7.
Look for the features you want only, Air Con uses petrol, cruise control you may never use and if it broke it'd take value off the car, electric seats if you're lazy! etc Buying a car with every feature could only mean misery as things do break on all cars and the more things that could break will break, and cost money.
Common parts with the older 800's (86 - 91) are a plus for a Fastback (like mine) or Saloon, the Coupe will cost more as it's much more different, doors in particular.
You'll enjoy the car, i know some people don't but it's big, fast, British and to be quite honest if i was in one of many other cars the other night it could have been a different story, the fiat that hit me was a total mess.
Have fun!