CraftyZary -- lovely work!
parlervousfrancais & others --
Can't speak for CraftyZary of course, but this focal-bead-holding wire ring project might give you an idea of what gauge to use : http://jewelrymaking.about.com/library/weekly/aa081501.htm
Btw, wire ring projects often specify a couple of specialty tools such as a metal ring mandrel &-or a rawhide hammer.
In some ring projects, I believe the mandrel -- & yes apparently it does need to be 'metal' not plastic --is used to put the ring on for hammering (with the rawhide hammer) for various purposes or effects.
And a mandrel 'might' help make easier/neater wraps around wire :
iirc, I think the basic idea is to put the thicker wire ring on the mandrel then use needlenose &-or bent-needlenose pliers & fingers (if needed) to sort of "weave-wrap" the thinner wire up-down-around between the ring & the mandrel.
I can see where the sturdy metal mandrel holding/stabilizing the ring so you could even use two pairs of pliers kinda makes sense ... although... guess you'd also have to stabilize the mandrel somehow, maybe in a vise or some such thing?
Couple of other pretty bead-holder type wire rings, in case anyone's interested :http://www.wigjig.com/jewelry-wire/ring.htmhttp://www.wigjig.com/jewelry-making/ring/pg06.htm
If you're already fairly experienced at wirework without a jig, you may be able to make these that way as well ... if not, maybe it'll inspire you to try a jig