Anna,
The Spagna Metro Station (Line A) is at the bottom of the Spanish Steps. As you're looking towards the steps, the entrance to the Metro station will be on your left. As I recall, one has to walk through a bit of "tunnel" to get to & from the station. Hiking up the steps with one small rolling suitcase wouldn't be a huge effort (at least for me).
Roma Termini is the largest station in Rome and is located in the main part of the city (as opposed to "the outskirts"). As someone else mentioned, the tracks all come to an end in the station, so trains have to reverse direction to depart. Termini is both a rail station and a metro station. The Metro lines are about two floors below the level of the main station. There are restaurants and other shops on the main level and additional shops (almost like a "Mall") the next level down. There are ATM's there also, if you'll need one.
Termini is the best place to buy rail tickets, as there are both "live agents" as well as ticket machines. You might want to check This website for all the details. Take a few minutes when you arrive to get your tickets to Florence. I'd suggest using the high speed EuroStar Italia / Alta Velocita as the trip is only about 1H:40M. The tickets will be a bit more expensive though, as compulsory reservations will be included in the ticket price.
I'd highly recommend that you pack along a copy of the Italy 2009 Guidebook, as I've found that to be a valuable source of reference during a trip.
Buona Fortuna e Buon Viaggio!