This is the same as any car you might modify, you start off by deciding how far you want to go, what the car will be used for and how much money you can afford to spend. The following recommendations are given without guarantee or warranty and must be carried out by a competent mechanic or experienced DIYer. The guide is designed to give you the maximum enjoyment out of your car while keeping it safe and reliable. It is aimed at producing a track-ready car which should prove durable. The cost of modification is greatly reduced by your ability and time willing to spend working on the car as well as having a dependable and reasonable local garage to tackle larger jobs or technically more proficient jobs like welding and braising. Remember you don't get anything for nothing.
Strada, 105TC and Abarth 130TC
Essentially I'm going to concentrate on the 105TC and 130TC model. Firstly let me say the lower range models with the SOHC 1.3 or 1.5 engines can be tuned, please follow the X19 tuning guide for this engine which can be located here. The options for these cars includes an engine swap to Uno Turbo power which are relatively straight swaps. In addition to this engine swaps to 2.0 8v Turbo and 2.0 18v Turbo power is possible as well as BMW V8 and Ford Cosworth YB. Obviously these are highly specialised jobs and extremely difficult to perform not to mention the budgets being required to support such projects. My web site details my own Strada which has a 2.0 16V Turbo engine.
In General I will stick to the hot models (105 and 130) which use the DOHC engine. The 105 and 130 differ more than you think, the 130 uses stronger front suspension, hubs and brakes of the 105 as well as a lot of minor changes and alterations to trim.
In general the tuning method is the same but the first thing you should consider with the 105 is sourcing 130TC carbs, manifolds and cams. This would see an increase in power of up to 15hp or more to 120hp. Then you would follow the Abarth tuning from then on.
These cars are very well set up as standard since they were designed for the enthusiast and homogated for racing. There are still improvements that can be made but in general don't change the car too much (like swapping the engine for a turbo engine) or that will devalue the car which is now a classic and becoming collectable in their own right. Modifications should be centred on improving the existing set up and extracting more power from the engine with an attempt being made to retain the original character of the car.
Low budget $200
Change the chokes and jets on the weber carbs and take them up a couple of sizes. Fit 34mm or 36mm chokes (13% or 27% increase) with an increase in main and air correctors by about 7% and 14%, you should then carefully check the engine responses and increase jetting from there upwards until the peak power is produced. Ideally set up on a rolling road with a selection of jets available. Power estimate would be about 140-145hp
People running Dollortos can perform a similar trick if you can find the spares.
People running Solex, you are very limited as spares are no longer available.
Medium Budget $1200 - $3000
Change pads high performance pads
Change the exhaust system for a stainless steel 2" two box system. This can be custom made using Jetex parts, labor will take about 3-4hours to make up. Parts should be 2 90* bends, 1 30* bend. 1 45* bend, two boxes and 1 meter of stainless tubing. This is sufficient to run the exhaust along the existing path.
Cam change to Colombo & Bariani inlet cam from Gazzella(UK) the corsa medio 11C3 profile with end slot. This should help increase power to 170hp
High Budget $3000+
Big brake conversion to Lancia Integrale or similar
15" X 8" with 205 or 215 section tyres
Guy Croft Stage 3 head, deck'd block to raise compression, forged racing pistons, Lancia Integrale flywheel and clutch (8v), power should be 200hp+