I hope this reply is not too late for you.
Tomatoes are deep rooted vegetable and as such requires a bigger container. Try container that is at least 16 inches deep and 20 inches wide at the top. See also Gardenmom's comments above.
I use commercial potting soil for container gardening. Try to keep the pH range at 5.5 to 6.8.
If you locate the tomato
plant inside the house, place it near a window that gets at lot of light. Tomatoes need at least 6 hours of bright-direct light per day.
I can't answer your question about grow lights because I never use them, but here's a link where you can compare different
Grow Lights .