Plants need basically three things. Water, light, heat. Anything beyond that adds to how healthy the plant will remain as it grows. A seed is self-contained food storage for the baby plant. The seed is large enough to get that plant growing and keep it healthy until it can sink its roots into the soil it assumes will be there.
So the seed won't start until the circumstances are right. Some plants need no light, or low light, or bright light for germination. Some need well drained soil, some need sand, or compost, and so on. But at the beginning they're all the same--light, water, heat.
In order to start a seed, you need to provide those three things.
Call me crazy, but I collect toilet paper rolls. Cut in half or thirds, they make perfect "peat pots" without the chemicals or the need to buy expensive specialty items. Stuffed with sphegnum moss (apx $3 per bag on sale, and a bag will last me at least two years) they create a place for the seed to rest, out of the water. The moss soaks up the water and keeps the seed evenly moist, as long as there is water in the tray.
My main tray for starting seeds is a rectangular cake tray from a grocery store. The base is black, the top is clear and it snaps on tightly enough to keep the water in. There are also no holes so bugs can't get in. A little water in the tray keeps my seedlings happy but not waterlogged. At full capacity it can hold about forty planting tubes.
The secondary seed nursery is also a cake tray, but this time slightly deeper. I can put the top on, but usually I use this one (or one like it) when the seedlings have secondary leaves and are ready to leave the sealed environment.
There they can grow until they are between four and six inches tall, depending on what I'm planting.
At that point I transplant them, into pots (saved from previous years) or into the ground. If I have two plants in each tube the tube is composted and I carefully separate the plants, keeping half the moss for each. Otherwise I plant the seedlings right in the tube. I have yet to lose any transplants this way, as the moss retains water even in the ground.
Gardening doesn't have to be expensive. It doesn't have to be difficult. By starting your own plants you know precisely what seeds are being used, whether or not fertilizer is used and what kind, and whether or not the plants are safe for your family.