Most veggies can be started inside for transplantation. This gives us an early start on the growing season. However, you have to be careful about sowing the seeds too early. Some crops don't take very well to languishing on window sills, if you know what I mean.

Watermelons can be started inside. They probably shouldn't be started much more than 3 to 4 weeks before transplant time, however, so you'll need to know for certain when it will be warm enough in your location. Many other crops can be started earlier and grown for a long time inside, given proper conditions.

Most veggie seeds (not all) germinate best when the SOIL temperature is warm....for watermelons, the warmer the better. However, you want the AIR temperature to be on the cold side. For many of us, that means providing some sort of consistent bottom heat, in the form of special heat mats or cables that you put inside the germination flat before adding the soil mix.

You also have to provide the most light possible, in wave lengths approximating the natural sun (if you don't have enough sunlight).

The only seeds I start inside are tomatoes and peppers. They are growing quite happily, full of promise (I hope) under lights. The rest of the garden will be sown directly in situ, at the appropriate time.

I wonder what kind of a spring we will have??

I generally start my tomatoes inside at the beginning of January. The watermelon will be fine if you direct sow it into your garden.

Here is a link that might be useful: Alabama Gardening Calander

I started several plants inside this year-
tomatoes (7 different varieties!)
squash
peppers
herbs

They're all under a warm white compact flourescent (Those spiral bulbs, ya know?) If they start to stretch I'll swap it out for a cool white. (warm white for seedlings, cool white for compact growth) and I set the flats on top of my aquarium lights until they sprout. Gets nice and toasty. :)