OK -- about to plant my first real garden, mostly just messed around before (experimented sounds better)...

I'm a little late getting started, but it is time to begin fall gardening in South Florida. I've thrown a few store-bought seedlings into my grow pots (I use the carbon felt-like ones) to make up for lost time. However, there are still a lot of varieties of veggies that I'd like to start from seed. The problem is this: it seems to be too warm outside (I made a moldy mess trying to propagate sweet potatoes this summer) and I don't have the room inside.

So my question is, am I going to have trouble direct-sowing cucumbers/zucchini/watermelon/tomato/pumpkin/peppers outdoors? If so, and I can find the space inside, do seeds need real lighting/tray setups to get started? I'm trying to keep my costs down and don't want to invest in a whole system yet. And, can I transplant seedlings a few days after sprouting or do I have to wait until they are 6" seedlings like I see at the store?

Any suggestions for an amateur would be helpful...