The reason to go to the trouble of starting plants from seed is that the great variety of peppers and tomatoes available. It’s fun to shop from garden supply catalogs and as you plan your purchases, consider a detailed drawing of your garden. This will also help as a guide when planting. When shopping, look for heirloom varieties which means you can save the seeds from a few good plants and plant them for free next year. While it is easier to just buy plants in May, it’s more expensive and the selection is very limited and boring.
Seed packs will tell you when to sprout the seeds, and also when to plant the seedlings outside. Peppers and tomatoes (at least) will need to be started from seed about two months before planting outside. Generally plant seeds indoors around March 15th and planting them outside mid-May or after the danger of frost has past.
To plant seeds, use a seed starting mix which is real light. We have two multi-cell containers with clear plastic tops that work well. Each has 36 cell packs which are good sized for the plants when it’s time to put them in the ground. After planting the seeds in the cells, I put a thermometer in there since our house is so cold, and the seeds need 70-75 degree temperatures to germinate. Place the flats in a south facing window. I put desk lights directly on them to keep the warmth and light going 24/7. Once the seedlings are all sprouted, they need some dark at night. Keep them moist by watering every day. Sometimes I use a mister to not disturb the soil nor seeds.
As the sprouts grow, remove all but one per cell. Once the second set of leaves have appeared, then you can remove the heat lights and clear covers. A cooler environment is good. Our problem is that we keep them in the warm indoor environment until planting outside. The best solution is to keep the seedlings a little colder, like on an enclosed porch. This way the plants grow very hearty, and thrive when you put them outside. Ours, being grown indoors for all that time, grow too fast and real tall and spindly. Then mid-May you’ll want to “harden them off” which just means putting the flats in full sun for increasing periods the week before you put them in the ground.