An excellent solution for germinating seeds and growing the seedlings during their initial phase is to use a Jiffy Seedling Greenhouse, or anything similar.
Benefits of using a Jiffy Seed Starter Greenhouse
Water wicks up from the bottom tray which promotes downward root growth
A clear plastic cover keeps in moisture during germination and first few weeks of growth
Minimal water maintenance compared to other methods
The trays can be re-used
Easy to handle, 72 seedling cells per tray (varies per model)