Welcome to TR. I don't know too much about Fiats. I used to have a '73 Triumph TR6 though. I imagine an old British car is only second to an old Italian car when it comes to finding people in the area that know these cars inside and out. I'd find someone familiar with those old Fiats to do the body work, not just a body shop. There are all sorts of nooks and crannies for rust to hide in that body-on-frame. And all kinds of weird hard to find parts that a specialist would know where to get. Maybe even a British car specialist could help if you can't find someone specializing in Fiats, as they are all pretty similar in their design.

Or put some ads on Craigslist looking for some help too. Good luck, post some pics, would love to see your fiat. BTW- there is a cheap Fiat Spyder on CL now, might be a good parts car for you.
1978 FIAT 1800