Hi, I agree with Derbyfella, if you really need an automatic, I would avoid all robotised manuals like the FIAT, and aim to get a car with a genuine automatic transmission (some Ford, Mazda) or CVT (Honda, Nissan).
As I understand the seals on the robots deteriorate with age, leaks cause gearchange problems and repairs are very expensive.
If your heart is set on a 500, the 1.2 is a good, tough engine, just make sure there's no oil and water mixing (sludgy coolant, mayo in the oil filler) and no unusual noises. There can be a slight rattle from the tappets on start-up, but if this goes away quite quickly as the oil reaches them, it's nothing to worry about.
Gearboxes are OK (the auto uses the same as the manual) but check carefully for signs of oil leaks around the transmission (especially with the auto robot, bolted on top of the gearbox).
I think they're well built cars, galvanised so rust shouldn't be much of a concern, but check the rear spring pans and coolant pipe between exhaust and engine for rust.
However, there are cheap components that can fail due to age or mileage. Suspension & steering components, brakes, sensors... it can add up if you need a garage to do the work for you, although parts are cheap.