That looks great! Especially for your first venture into bead-land!
As for your question, usually if you're using 21g headpins and beads that size (they look like 4-6mm beads with size 6 seed beads), a single loop should suffice. As was posted earlier, wire-wrapping is a lot easier if you're using craft wire vs headpins. Headpins / eyepins tend to be much stiffer than craft wire, even if they are the same gauge.
I've been working at a bead store for 5+ years, and I usually suggest to people to try their hands at wire-wrapping using 22 gauge craft wire. It's cheaper than headpins, you can practice making a bunch of links with wrapped loops on both ends of the bead, and once you're done practicing you can attach all of the links together using jump rings (or by making more links) and make a necklace / bracelet / whatever.
Another reason I suggest learning on craft wire is if you cut a 1 foot piece and start making links from that, it will really help you judge exactly how much wire you need to use to get uniform matching wraps every time (I usually shoot for anywhere between 2-3 coils per wrap), and it cuts down on wasted wire.
Hope this helps!
*edit: spelling mishap!