Hi Ballerina. Welcome to the forum and to vegetable gardening. I've always said that growing your own veggies isn't really any better for your physical health, but it does wonders for your mental health.
I start tomatoes & peppers indoors around the end of Feb/early March. Peppers especially seem to need an early start. I've never used heating mats, and we keep our house on the cool side (64*).
The seeds don't need light to germinate, but growing lights will make them grow more vigorously once sprouted. With a window with good southern exposure, you may get by without extra lighting, but the plants tend to get "leggy"-- tall & spindly.
Also, make sure your plants are well ventilated to help minimize risk of mold killing 'em.
Transplant outside after the last frost. Be patient; don't rush it (and don't ask me how I know that. Fools learn from their mistakes. Wise men learn from the mistakes of fools.).