Your lights must be close to the plants. To do it well you will need 4 bulbs side by side for one flat. However if you used 4 bulbs you could do 3 flats. The end of your flats need to hang over the flat a few inches. You will not burn your tomatoes with grow lights. You can germinate with cool white lights. I think the other trick is to time it just right so that they don't out grow the amount of light you'll need for them to be surrounded efficiently. You will need to transplant also which means you must prepare to have more lights as they grow or just start smaller. How many flats do you plan on sowing?

It is my opinion to use smaller containers to start seeds in so your seeds wont rot. It gets to me a juggling act too to keep them at just the proper dampness. Use a spray bottle to mist them frequently on top. You don't want the mmedium soaked. Be sure to use those doam lids as they hold in the right amount of moisture.

If you haven't invested in heating mats it would be an excellent investment, trippling your germination rate. They are inexpensive if all you want to do is increase the ambient (surrounding temperature in the room) up 10-15 degrees. Once your seedlings germinate you're done with the mats. I'd be careful using bottom watering until you at least have germination and becareful not to over water.

You can also make a tent to keep the right moisture in the rooms. At this time is is of the utmost importance that you do not let the top of the seedling medium dry out or the seeds may be cooked. You must check them once or twice a day. take off the domes and give them a good mist. You can get hydrolic misters for 6 bucks at Walmart but I doubt they are in stock, just get a good spray bottle. Too much water is another major culprit for leggy tomatoes. My suggestion is to sow about as half as many seeds as you have lights for now because once you start transplanting your seedlings will take up twice the amount of space.
Another trick is to transplant a tomato plant deeper than it was grown, this goes for anything transplanted for the most part. Always pot up one size larger. It is important the plants do not sit in mushy medium. You may also pinch off a couple new leaves, this also helps to bush the plant out. I'd wait a little while though. Also don't over plant, or if you do get rid of the weaker ones early enough they are not affecting the nearby ones. Instead of pulling them out snip them off so as not to disturb the soil. I would also start fertilizing a weak solution. Look into what is best at this time. Be careful of not too my nitrogen so you don't get a lot of green but not fruit. (Research the best fertilizer for tomatoes sprouts. Some are for healthy root development, which maybe you want now. Whatever you choose dilute the solution about 1/4 and give it to them every time. the bottom watering suggestion is good but keep the mats handy incase your medium gets water logged and you have to evaporate the water fast. I prefer a heavy mist until I have reason to believe roots are extablishing.

I've grown many things in the basement, many heirloom tomatoes, so good luck, I'd get grow bulbs with the whole spectrum of lights, but cool white will germinate the seedlings due to the plants don't need light to germ but heat. Good luck, hope this has been helpful,
Micki
Of course harden off your seedlingsusing your coldframe. I'd love to make a coldframe. Yours sound like the ritz. Have you considered Winter Sowing your seeds? the benefit to that is your seedlings will be stronger and heartier. Here's a link you might be interested in. I'm sure your cold frame would be put to much good use, and you'd eliminate the problem of the seedlings being spindly. Winter sown tomatoes don't germinate as fast but because they have been grown with Ma Nature they are much hardier and catch up to their counterparts,
Let me know what you think,
Micki

Here is a link that might be useful: winter sowing tomato seeds

Hello neighbor! Is this your first time starting toms from seeds? I've started a few, and here's what I've found, especially for our neck of the woods.
I would wait until at least April to start any seeds. I had the same idea you had and started last week of March my first time and they grew WAY too big to have inside the house. Once they germinate, they grow very quickly. Mine got huge without being under lights towards the last 3 weeks because they were too tall for my shelf. I stuck them in my 3 season porch and they continued to grow until the last weeks of May when they went out, at almost 2' tall!
I suggest starting no earlier than mid April, since even if you have lights, they still get leggy because they are such sun lovers. Also, toms don't do well with nighttime temps less than 50F, so in my area outside of Boston, that still means I don't set them out permanently until Memorial Day, hence the mid April sowing. They take 4-6 weeks to be ready for transplant.
I did not use a heating mat to start the seeds; just sow and they came up inside my dining room, which is around 67F. Kept them moist with some plastic shrink wrap over the top and took the cover off as soon as there was a sprout. Just watered from the top when the soil dried out some. I did however grew them in potting soil, not seed starter mix, and there was no shock from transplant. Since there was slow release fertilizer already in the mix, I didn't do any fertilizing until they were outside. I also plucked off the bottom 2 leaves when I transplanted from a 3" pot to a 6" pot, and then again when they went out to their final containers. I started the seeds in the 3" pots. Since I had them out on the porch and in the sun during the warmer days of May, that hardened them off for me.
Oh, and drainage, drainage, drainage! Make sure you at least add some more perlite to the mix you buy or mix so they aren't standing in water. Keeping moist in one thing, too wet is another.
Good luck with your upcoming tomato jungle!