We have a Mk1 punto with 100k+ on the clock and it runs a treat. It is very well looked after though.
Spend a few quid and give it a decent home service. Change plugs and leads, oil and filter, air filter. Take off breater pipes and clean them out if they are blocked or have mayonnaise in them. Check all vacuum pipes are in good condition and have no leaks. Take air box cover off the injection body and check the seal isn't borked and actually does seal the airbox to the injector body. Check the foil tube that draws hot air from the exhaust manifold in the winter is in good condition and not split.
Also, check to see if the modifications have been done on the radius arms to stop them failing the MOT on knackered bearings every two years. About £15 to get the modification parts (two rubber cups, one for each side) from FIAT garage and fifteen minutes to put on yourself.
Do all of the above and you should get a few more years out of the motor (change oil and filter regularly). I've worked on loads of cars, and the punto is one of the easiest to work on and one of the cheapest for parts.
