Immediately. I started seeds June 15th. You can start seeds probably into the first week of July.

Read Growing Tomatoes From Seed. Very important that you start indoors in SOILESS seed starting mix, water properly but not overwater, and grow the seedlings under intense fluorescent lighting for 16 hours a day until you start hardening off (Gradually expose the plants to sunlight over a period of 1 week).

You will want to pick varieties that do well in Florida and at the same time, have ripe tomatoes BEFORE the first frost this fall. So generally you want smaller to medium size varieties. I am finding that what I grow in the Spring and what I grow in the Fall are going to be quite different.

I'm thinkin' Stupice (small Russian variety), Anna Russian, Eva Purple Ball (very tasty pink fruit), Creole (takes the heat and keeps on pumping out flavorful medium-sized tomatoes), Jet Star hybrid (early ripening), Sungold (tremendously productive, tasty orange cherry tomato). If you must have a beefsteak/slicing tomato, you can try Gregori's Altai. Azoychka is a tasty large yellow that matures early.

I would highly recommend posting a question on the Growing Tomatoes forum about which varieties you might consider for fall growing in Tampa. The reason we can't generally grow tomatoes all summer in Houston is that tomatoes really need 2-3 days in a row of 80's (not 90's!) with evenings in the low 70's to set fruit. If it's 95 degrees every day for weeks with no break, tomato plants start to give up the ghost and their pollen doesn't work.

Where to get seeds?
Seed Savers Exchange
Heirloom Seeds.com
Tomato Growers Supply

Thank you so much for all the great info. I really appreciate it.

hate to be a bore, but i have never faffed around with tomato seeds like that. i just plant them in compost in a seed tray, and most if not all seeds have grown, and fruited. ive even had them grow from a lost tomato that found its way into the soil outside, so dont worry yourself about them

Yea....I agree with hjm202....

I had near 100% germination on 80 plants (17 different kinds - mostly heirloom varieties) using the Winter Sowing method outdoors last spring BEFORE the last frost....(I just covered them at night). They were the toughest tomato seedlings I have EVER seen....TONS of roots at plant out time, too (potted them up 3 times prior).

Easy, easy...almost too easy...LOL!