Traveling from Florence to Lake Garda
Ciao AliceLondon and welcome to the forum!
The best and fastest way to travel from Florence to Lake Garda is by car, I suggest hiring a car while in Florence and head on directly to the Lake, it will take around 2 hours and half driving.
With a car you can move freely and visit all the lovely villages facing the lake, above all Sirmione.
For information on renting a car you may find this link useful:
http://www.discovertuscany.com/tuscany-car-rental/
Of course, considering that you are on quite a tight budget, renting a car can be convenient only if you rent the car just for very few days, otherwise it's better moving by train.
From Florence's Santa Maria Novella train station you can take a train heading on to Desenzano or Peschiera del Garda train stations, both located along the southern cost of the Lake. While Rovereto is the train station on the northern coast of the lake. From Florence, however, you need to switch train either in Podova or in Bologna, and from there take the train to Desenzano or Peschiera del Garda.
The total journey will take about 3 hours. You can then reach by bus all the other main localities on the lake.
You can check train schedules as well as tickets' fares at this link:
www.trenitalia.com
In case you need additional advice regarding accommodation or anything else, just post again
Have a nice day!