If you want a country that starts weak but gets really strong, Byzantium is the perfect choice.
however there are lots of countries that are fun to play and can get really strong : England (you can either be historical or win the hundred years war, getting cores in a lot of France with a mission. to get the mission : get at war with France, use the reconquest casus belli -> cancel your current mission, you'll probably get the mission to ocuppy Paris, just do that and have fun with your new cores

)
Bradenburg (Prussia -> Germany and nothing stops you after that!)
Byzantium (like i said before)
Castille
Milan (or some other italian country)
Muscovy (Russia is a monster after you get Siberia)
Brazil (or maybe others american revolter countries, start at 1750 with Portugal and trigger the event using the console. I said Brazil because it's in a very good position to colonize South Africa and then India. plus Brazil is just awesome

)
among many other countries...
however i think Genoa has no fun missions, unless you're mentioning Geneva as the tiny country between France, Burgundy and Switzerland in MEIOU.