When growing your Vegetables from seed, you will need to provide a place for them where they will receive enough light and water to grow. I have placed mine in a south facing sunny window, and they grew ok, but they seemed to bend over towards the light, and they also were pretty weak. So that is an option if you don’t have any other options.
I recommend building a light garden. When we first started growing from seed, we built a light garden frame out of pvc pipe, and hung the lights from the top bars. That worked well, and we used it for many years. But then it started to fall apart, and there was also the issue of where to put it when it was not being used. It took quite a bit of space and we did not want to disassemble and reassemble it every year. So we decided to buy a shelf that was 4 feet long by 2 feet wide. Then we measured out were to put hooks, and screwed in the hooks and hung the lights. It is fairly easy to take apart if needed, but it can also be left and used as shelves for the rest of the year. I particularly like this because we can have 2 levels of light garden or more if we wanted, and it also gives us space to store the seed growing stuff above it. It is a little bit of an investment, or if you already have a shelf, then it is even better. It does not have to be the same kind of shelf; you could find hooks that would work for hanging the lights for the metal shelves, and even the plastic ones. It should be 4 feet by 2 feet to work the best.
As for the lights, regular florescent lights work well, but we found you need the kind that has wings on the side to direct the light down. We tried the cheaper kind that doesn’t have the side wings, and they do not work very well, the plants really suffered. We also use a timer for the lights and they should be on about 16 hours a day to give the seedlings enough light, and have them about 2 inches above the plants and slowly move the lights up as the seedlings grow.
Check the moisture of the soil every day, they will need to be watered often, and it will greatly stunt the growth if they dry out too much. Watch for when they need water every single day, which would be the signal that the plants need to be transplanted into a bigger pot. Keep them in the right size of pot to avoid them getting root bound and possibly stunting the growth.
It is very rewarding to watch your plants grow from seed, and once you do it a few times, it becomes second nature. Happy gardening!