There are only two requirements for containers to start your seedlings. They must be scrupulously clean, and afford proper drainage. There are two main styles, seed trays or flats, and individual seed containers. You can buy them new, clean used ones, or recycle empty yogurt, milk and similar containers. A solution of 1/8 cup bleach to 2 gallons water can be used to rinse used or recycled containers after a soap and water cleaning to prevent disease.
No one perfect medium exists. Seedlings thrive in a moist, spongy growing medium. "Soil-less" mediums work really well here, and usually contain a blend of vermiculite, sphagnum moss and/or peat, and Perlite. They work better than garden or potting soil, as they retain moisture, provide good aeration, and reduce pest and disease problems. You can mix your own using 1/3 to l/2 sphagnum moss or peat, and the remainder vermiculite or Perlite. Ready-made mixtures like Pro-Mix work great and are readily available. Whatever you use, it MUST be sterile.
In order for a seed to germinate, it must be mature and viable, and
receive the proper combination of moisture, temperature, light, and air.
Most annuals, vegetables and herb seeds germinate easily. However,
there are some that need special attention. Perennial seeds, in general,
need more attention than others. Some seeds may need either complete
darkness (Calendula, Bachelor Buttons, Larkspur) or constant light
(Snapdragon, Petunia, Yarrow) to germinate. Some need to be soaked
(Parsley, Asparagus, Morning Glory) because their seed coats are very
hard, preventing moisture from getting through. Some seeds may contain a
chemical substance that inhibits germination. Soaking is then needed.
Some seeds need stratification, a cold
treatment, before sowing (such as Echinacea, Lavender and Columbine).
Some seeds need scarification (Lupines, Sweet Peas), by nicking or
filing, before sowing. Some seeds need cool temperatures to germinate.
Examples include Rosemary, Lettuce, California Poppy. Some seeds do not
transplant well and should be planted in peat pots, examples being
Nasturtium, Dill, and Poppy. This information is usually provided in the
seed catalog, on the seed packet, or in a good gardening book.