Super post there Biz

I've met up with probably the same 'Uno Turbo guys' in Jo'burg

One car had 'Yokohama' plastered all over it and another was dressed up in Speed'n'Sound livery. That was a few years ago now though!
Reality is that there's no easy answer, especially when you're starting with an engine that has 334,000km. Personally I'd get hold of another engine that's done fewer kilometres, and rebuild that with standard replacement parts where needed. I actually agree with the advice to try TurboCollective, even though I've hardly ever been there, I'm sure it's inspiring to read about big-budget modifications.
I guess I'm getting old, because I've decided to stick with the standard engine/standard turbo. It's rare to get something for nothing in this world, and a bigger turbo brings the problem of greater turbo lag. The standard turbo comes in with enough of a rush for me at 2000RPM, I don't think I'd like even more of a rush starting at 3000 or 4000RPM, it would reduce the driveability. Also, my particular Uno Turbo is amazingly economical (as much as 50mpg in open-road driving) and I don't want to endanger that.
However, like most owners, I fitted a bleed valve (boost controller), in line with the wastegate actuator. Even at the 7000RPM redline, the boost tends to go over 1 bar very easily and I have to adjust the valve carefully. I think the large exhaust (fitted by the previous owner) helps to liberate more boost from the standard turbo (but I could be wrong). After fitting a cone air filter (under the left headlight) I found that the boost needed reducing again. Therefore, these mods (big exhaust, cone filter) that normally produce little effect for non-turbocharged cars actually have quite an effect on the Uno Turbo. The best news is that when driven gently, economy isn't affected.
However, the big exhaust makes a tiresome droning sound on long trips, and the cone filter probably doesn't filter very well and would be a bad idea for a dusty environment. Always remember that FIAT weren't stupid - there is always a reason for the choice of standard equipment...
Water injection - keep searching. There was a South African page (the Abarth club?) that had great info on this. I'll try to find it for you.
EDIT: While I can't find the original page, I have found the same well-written text copied at
http://www.tuning.bg/forum/viewtopic.php?p=31683&sid=0b1b6705661b08dddc65a697c0dc60e7 - I suggest you read it carefully
I think the best way to add performance is to reduce weight. Mine's down to 920kg measured on a weighbridge with me (73kg) and fuel (28kg) on board. Last time I measured it, it was 1000kg. According to the handbook, the standard weight is 895kg, so that's about 80kg saved by removing rear seats, soundproofing, stereo speakers, and unnecessary brackets. You could probably manage quite a bit more by fitting fibreglass panels (e.g. doors, bonnet) and plastic windows. As for the difference this makes - find yourself an 80kg passenger and go for a drive with, then without them.
Rather than creating more engine power, I feel that there's bigger gains to be had from improving the handling - lower the centre of gravity, fit stiffer suspension at the front, but do it all really carefully so you don't end up with a roller skate that snaps into oversteer at the slightest provocation. I think the back end needs to be softly-sprung so as not to overtake the front end... you want the back end along for the ride, but not locking up under braking or jumping sideways over bumps.
The best improvement is when you fit race tyres - "For competition use" - the ones with a treadwear rating of 50... Those alone improve the handling more than anything else...
If you want to build a 1600cc FIAT Tipo-style engine and turbocharge it, that can be done too (forged pistons, head gasket shim) but there will be many judgements to make on which parts to replace, head machining, checking the 1580cc block for warping, etc. You need someone to give you this advice in person - someone local to you who builds high-performance engines and knows FIAT engines well.
I think the forum is really valuable for advice, problem-solving, and ideas - but to manage a whole project, you'll need local help. However I look forward to be proven wrong when knowledgable Turbo-tuners read this thread. You have to be patient
-Alex