Firstly, how much do you want to spend? A coop can range from £2500 up to £9500, so you need to think how much you are spending. Cheaper ones can be dogs and will need alot of money to get them right. I would spend as much as you can to get the best availble in your price range
Things to look at:
Belts should be done every 5 years or 72k miles, some people do them sooner, but thats the Fiat recommendation. Make sure when the belts are changed the invoice is for aux belts, pumps and all the other bits, not just the cambelt, it is rarely the cambelt that fails.
Red key, thats up to you, a new red key can be got for £200, I don't have one, lots of oether people don't have one and never need one, I wouldn't let this put you off of a car.
Check the oil, oil should be changed every 6 months and needs to be topped up every 1,000 miles or less.
Other things to look for are worn suspension / wishbones - can lead to a crashy ride, std exhausts wear out and fall off and melt the bumper, tyres are £100 a corner so check them. Check the manifold doesn't tick from cold start up if it does it means its cracked and you'll need a new one or a good welder.
A good service history, ideally by a fiat specialist and not Fiat, is essential.
For turning the power up, to start with I wouldn't bother, you will already be in a 6 second to 60 car that is cable of 155 mph. Howvere for £30 you can drop a chip in to give you an extra 30 bhp, but then you'll need a boost gauge to check your not over boosting, then if you are you'll need boost control to stop that. Then you'll want to whack the boost up from 1 bar ot 1.2, so you will need extra cooling, etc, etc, its endless. Its easy to get to 260, but 280 and above is a little more trouble.
I am running somewhere near 300 bhp, this has probablty cost close to £2,500. Some are running 500 bhp, this costs a tad more.
A good resource for the fiat coupe is
http://www.fccuk.org/forum/ubbthreads.php maybe have a look around there
