Start tomatos from seed 6 weeks before your plant out date. Starting earlier will result in tall, usually leggy plants.

Your goal should be to have a plant around 6" tall and sturdy at plant out time.

Starting them in a windowsill is unlikely to be enough light for them. A cheap fluorescent shop light hung 6" over the top of them would be much better, but still won't be enough light if they grow much more than 6" tall.

In the event you do end up with tall, leggy plants you can bury the stem without harm to the plant. It's called trenching and you just lay the plant on it's side in the trench and cover all but the top 2-3 inches. The plant will grow upward by itself so no need to bend it upward, just keep the leaves off the ground so rot doesn't set in (just put something like a small sheet of plastic under it).

Pot size with tomatos is flexible. I start out with a normal seed tray (6 pack) and transplant into 20oz plastic cups with holes punched in the bottom once the plants are a few-several inches tall. That's all I do until they get planted outside. You can use the 4x4 pot as well, but tomatos are a plant that benefits from having it's stem buried which is why I use the deep cups. They form roots along the buried stem. You can help the process by clipping off any leaves that would otherwise be buried.

Put 2 inches of potting soil in a 16 or 20 oz cup. As the plant grows, cut off the lower leaves and add more soil a little at a time. On warm afternoons, take them outside for a couple hours. Don't forget to bring them back in. They'll freeze. Use a lamp if you think they aren't getting enough light.

I don't think light from my window is an issue. They'll get just as much as they did in the yard last year and they did fine. It's not leggyness I'm worried about, it's them getting too huge.

Some years when I do transplants I pot them to a 1 gal. black pot and then to a 3 gal. if needed then on to the final 20 gal. container. The trick I have found is don't let it get rootbound or slow down growth. I have started seed a early as late December but more often mid-Jan. for a final plant out in mid-April here in south central Texas. By not letting the root system or top slow growth and not giving much cool weather it is flowering and setting fruit by early May. We have a short spring growing season before it gets too hot and fruit set stop often in June many years so getting a jump for us is critical.
Hope this gives you some food for thought on your question.
Happy Growing David