I'm not sure if you really meant a 'vintage' Fiat Cinquecento from the old days (1957-1974), or the new Fiat 500 (2007- present), which is the modern car that is designed like a 'vintage' 500, but a very modern car.
If it's truly a 'vintage' car from the 1960's/early 1970's, the car is much smaller, the trunk (if you can call it that) is in the front while the engine is in the back. The cooling system is not a cooling liquid, but air, and the engine is likely to heat up in very steep hills. The power is very low, because the car had only 2 cylinders with a total displacement of, you guessed it, 500 cc (479cc to be exact, or 499cc in the 'Sport' model).
But the thing you should know is that the car had an unsynchronized gear box mesh, therefore in order to change gears, you need to become familiar with the 'double clutching' technique ('doppietta' in Italian). The way to do it is by depressing the clutch once, to disengage the gear and place in neutral, then depressing again and engage the gear. The movement takes place in a very short time. It took me a few tries to learn it with my dad as my teacher (he used to drive city buses in Florence at the time, so he was a good teacher since the old buses were also unsynchronized). Read about it and test your skills on a manual transmission car before you go. Failing to double clutch will result in 'grinding' the gears ('grattare' in Italian).