Although I have owned many over the years I haven't put huge miles on any of them. My current X and my last X were both my daily drivers for extended periods (during the spring summer and fall) and neither of them left me stranded ever. My VWs have always been more problematic with some of their fussy engineering.
My experience with Fiats when I buy them has been:
Replace the maintenance items. Go through the primary systems and replace the soft parts (belts, hoses, flex lines, fluids, plug wires, dist cap, rotor, plugs, filters. new pads, new rotors) flush all the fluids and verify things are working. Repair what is clearly broken.
Fix the stupid things previous owners and ham handed, know nothing mechanics have done to the car. This usually takes longer than the first list and a whole lot more head scratching.
Tadaa! A pretty reliable car.
Which may need more maintenance than a 2010 Toyota, but not much more than a 1984 Toyota would have been. These cars are basically simple, there is no multiplexing in the electrical system, the FI is very simple and uses simple switches, relays and rheostats to function and the mechanical parts (on a 1979 and newer) are pretty robust and well made. Some of them are hard to remove I must admit.
When Fiat went to electronic ignition, particularly the Bosch set up in the X, reliability went way up. With the ultra simple Bosch LJetronic fuel injection it went up even more, presuming it was even slightly maintained.
The biggest ills of any Fiat are of course rust and lack of maintenance. One of those maintenance issues is of course cleaning grounds and ensuring things that need power get and have a way to return it. A couple of ways drivers kill their Fiats is to: ignore the timing belt (trashing the valves and sometimes the pistons), ignore the cooling system (congealed coolant with no corrosion inhibitors or large air pockets) and shifting too fast (destroying the syncros in second and third) these cars are never going to win the stop light grand prix and no amount of fast shifting will do so.
Will there be challenges in performing all of this? Absolutely. Will it leave you by the side of the road, maybe but so could a lot of other cars from that same era. My experience is that if it starts, it will likely keep running until I shut it off.
Look at the many posts of JVanDyke for a primer on a someone who has resurrected a long fallow car using perseverance and methodical chasing through the car. Fixing a car, any car, is a logic problem, nearly every part follows a sequence. If this switch opens then "that" should happen, if it doesn't then something between the two elements has failed, find that failure. Becoming familiar with the systems and their relationships to each other will be among your best and most important tools.
Sorry for the lengthy post. Good luck with your coming project.