Cheftang Welcome to FT
Swiss Airlines, Lufthansa & UA are star alliance
AA (and BA & others) are Oneworld alliance
USA based airline ffp's tend to be more generous (status benefits/earn/burn/upgrades/award cost/award cash surcharges/expiry/affiliated
credit card ff mile earning/promotions) compared to non USA based airline ffp’s (even after the recent changes to some USA ffp’s). But if you are not flying the airline of your ffp the useful benefits are somewhat limited. Low cost fares are tending to earn few ff miles, but depend on the ffp. Earning miles from non flying activities is easier with an airline ffp of your home country.
When you state
"Would prefer to fly business class when available, but will settle for premium economy when the price is prohibitive." do you mean when paying cash money?
Or hoping for business class/real PE award flights? [hard for 3 people]
For awards Florence airport only may limit your options. Another airport & a train ride may be better
https://en.wikipedia.org/wiki/Florence_Airport
Credit card transfer links
A guide -->
https://www.awardhacker.com/#f=San%2...=0&c=j&s=2&p=0