You don't have to wait. Drying seeds is only needed if you are going to store them.

Any good seed starting medium is good but you also have coir, oasis cubes, sponges, peat pellets and a bunch of other options. There is also a method to sprout seeds in a coffee filter in a baggie. It's called "the baggie method" and it's in the FAQ. I think it's in the Growing from Seed forum.

I little hint if you're new...if you use a peat based medium (most are peat), hydrate with warm/hot water. Cold water takes a long time to soak into peat.