Well where do I start. The problem with the standard transaxle is that it has too high a final drive and there is a large hole between 3rd and 4th gear.
Abarth made 4 speed and 5 speed transaxles. A ggod combination is a 4 speed close ratio gearset and a 9.39 ring and pinion. You can retrofit these parts to a standard Fiat transaxle for probably around US$2000 or less. This will give you good top speed and get rid of the hole in the ratios.
Of course a five speed is great. There is th original Abarth box (only used or abused available) and it will likely set you back from US$3000-5000 dollars plus rebuild costs.
Then there is the Collotti box. OK but VER EXPENSIVE.
Then there is an Italian maker of a 5 speed at around US$4000
Note: Both of these will require minor body mods and shift linkages to be reworked.
Finally you can do as I did and graft a Punto front wheel drive 6 speed gearbox to the differential of the standard Fiat 600 transaxle. All you need is the parts, a damn good machinist and about US$3000
Hope this helps.
Paul vander Heyden
Scuderia Topolino
www.scuderiatopolino.com