In the case of gardening, most people start with seeds. You can start with transplants, (little plant you buy at the store usually in a 4 or 6-pack) but those get transplanted the same way our seeds will a little later, so we will get there. I prefer seeds for a number of reasons:
1- Cost. It's much cheaper to buy seeds than plants.
2- Variety. Most home improvement stores have a wide selection of seeds of virtually any vegetable you can dream up. Seed packets require no maintenance and very little space. Plants, even seedlings, require daily watering, sun exposure and space for pots.
3- Satisfaction. There is something about seeing a seed turn into a seedling which grows into a plant that produces food for your family.
So for starting seeds...
You will need:
Seed starter. I prefer organic seed starter. I usually buy it when it goes on sale at the end of the season (August-November) and store it for the following year.
One really cheap "greenhouse" to make is a milk jug greenhouse.