Are we talking about the Fiat500 or the Fiat500X. Those are two totally different cars. The Fiat 500X is a crossover that is larger, with adequate cargo, and much more powerful that a Fiat500, which is basically a toy city car for commuting, and not really adequate for any luggage larger than a briefcase.
I would put the Fiat 500X and the Jeep Renegade in the same category as small compact SUV/crossover. The Fiat Grande Punto is also in the same category, although not a crossover and it is out of production so you won’t get it anymore. The Punto Estate is a larger station wagon. All of the above are adequate for mountain driving (have enough power) and have luggage hold sufficient for at least 2 or 3 if you fold the back seat half. I was able to fit 4 people with carry on luggage in a Renegade and in a Compass. The punto estate is large enough for 4 with luggage.
The Fiat Panda is a piece of krap in terms of torque in my book. No power at all. It has a small cargo hold, but enough for up to 3 people by folding half seat in the back. But can a Panda climb the Dolomites passes at over 25 miles per hour? Doubtful.
I don’t have experience with the Corsa or the Ypsilon or even the Peugeot208. They are small however.
Personally if there are two or three people traveling I would go for the Jeep Compass, Jeep Renegade, Fiat500X, or Fiat Punto. The Compass and the Punto have the largest cargo of the group. If you rent in the Compact/Small SUV category the above are cars that you are very likely to get, because they are all manufactured in Italy by Stellantis Group, which is big in Italy (Stellantis is the conglomerate born from the merger of Fiat Chrysler and Peugeot-Citröen in 2021).
To rent a car in Italy I use a broker called www.AutoEurope.com then select the best deal in the Compact/SUV category (which I recommend for the Alps) usually with Hertz or Avis or Europcar. You are not assured of the exact model you will actually get, as they can give you anything similar in that category, but so far it has always been either a Fiat 500L, 500X, Jeep Compass, or Jeep Renegade, all of which are manufactured in Italy. Once I also got a Opel Mokka, Opel is another Stellantis brand, and the Mokka is manufactured in Spain. The Punto Estate is probably a step above, because it is a larger station wagon. Rental companies like to have cars in their fleet that are easy to resell in the used car market, and the above models are all very popular in Italy. If they give a diesel you will have even more power and torque for the mountains, however rental companies are getting away from diesel cars since local governments have placed a lot of restrictions on diesel,cars in the city centers because of environmental concerns.