As you say, there are three "trim" levels on Corvettes built at the factory. So far as I'm aware ALL official European cars are LT3, which is the highest level.
Regarding the mechanical stuff there are essentially three levels of car built at the factory,
Base model - wet sump, modest brakes, no/small rear spoiler. (Base car has never been sold in Europe.)
Z51 - same engine as base model but with dry sump system, bigger brakes and a spoiler all the way across the back of the car.
Z06 - bigger engine, uprated everything, wider body, front splitter etc - and a lot more expensive.
The easiest way to tell an official European car from a personal import is to look at the door mirrors. The mirrors are significantly larger (deeper) on European cars. Euro cars will all have headlamp washers, US cars may have them (although probably not).
Regarding transmissions, the earliest auto C7s will have a 6-speed box and later cars have an 8-speed paddle-shift box. All manuals are, I believe, the same.
Most cars you find for sale in UK will be at least Z51 with LT3. Check carefully if you find a "cheap" car because it may be either a very low spec' import or a write-off that's been repaired and then exported to a market where its history is less likely to be checked.
Unless you want one of the fastest cars in the known universe you'll probably be looking for a Z51 with LT3 and a transmission to suit your taste.