I almost exclusively use a standard wooden hoop that can be found at most craft stores.
There isn't a right way to frame or hoop your embroidery while you work on it. But you may find you prefer one way over another.
Embroidery needles (as opposed to other types of hand-sewing needles) have a larger eye to allow for thicker floss to fit through.
Embroidery floss has six strands twisted together. After you cut a length to stitch with, you can separate out just the strands you want to use at a time.
A good rule of thumb is that the more strands you use, the wider area you can cover with one stitch. This means you can make thicker, bolder lines or cover more area with fewer stitches. For fine detail work, use fewer strands. For emphasis, use more.
My patterns have information about which DMC color embroidery floss I used to create sample. Either look for the DMC brand, or a brand that lists its corresponding DMC number.
Any woven fabric will do in a pinch. I prefer solid color cottons with a tighter weave. I find a lot of inexpensive fabric at the thrift store and my local reuse store (SCRAP).
I go into more detail about different transfer methods here.
TL;DR version: A solid choice is always a water-soluble fabric marker to trace the pattern using a light box or window.