I am traveling with 3 other ladies to Italy, Croatia, Austria. Should we purchase train tickets before leaving the
USA? Would renting a car be better?
Renting a car in one country and leaving it in another will be expen$ve-- typically $800+, just for the one way drop fee, on top of the regular rental fee.
Depending on where you are going pre-purchasing train tickets may save money.
For a better answer to your question(s) you need to provide more details about your travels
Without some knowledge of your travel plans, impossible to answer. Car is more useful in the countryside where you don't have established public transit and nearly worthless in major cities. If you purchase ticket prior to departure, you often can take advantage of deep discounted tickets that are not available the day of travel. But those tickets come with heavy restrictions.
Thank you!
Long distance train tickets are usually (depends on the rail company) cheaper if bought in advance. And the best place to buy is the rail company's own website.
I suggest you read the "Man in Seat 61 website, especially these pages
General "how to buy tickets": https://www.seat61.com/Europe-train-tickets.htm
Italy specifics: https://www.seat61.com/Italy-trains.htm
Croatia: https://www.seat61.com/international-trains/trains-from-Croatia.htm
Austria: https://www.seat61.com/international-trains/trains-from-Vienna.htm