To be specific, GSG refers to "Great Southern Gathering" which is apparently where the weave was invented/perfected, and is almost identical to Half Persian styles. I think what you've got there is just... a small piece of HP3-1
I started with galvy too, for cheapness and being available locally. Fun enough to work with, cheap enough to experiment with. The gauge actually depends on what gauge. There's American Wire Gague - AWG, and standard Wire Gauge - SWG and honestly I have no idea what the differences are. It's also entirely more common to put inch fractions or mm units, like 11/32" instead of saying .34375, although I'm curious how you ended up on that specific ID because that sounds a little obscure.
Regardless, get some saw cut aluminum rings and some toothless pliers. At Theringlord.com I got two pairs of pliers for $6.05 each, which is their generic brand but they have pliers going up towards $75 I think, and some 18g 1/4" saw cut bright aluminum for $1.70 per ounce, and being that aluminum is very lightweight, that's like 400 rings per ounce, and I figured a E4-1 bracelet for my 7" wrist cost ~65 rings, so you do the math there on how cheaply aluminum pieces can be made. I also got .5oz of 20g 3/32" saw cut aluminum that cost $7.30 per ounce, but that got me like over a thousand micro rings as well.
Either way, getting some aluminum is very nice, it's cheap, light, doesn't tarnish or rust, and it's strong enough for casual jewelry. I'm going to order some colored rubber rings and some colored aluminum rings, and make bracelets without clasps that just stretch because of the rubber. For quality though, swapping to stainless steel or silver, or even niobium can do you a lot of good to increase value and strength. Remember, a lot of people will buy something expensive for the sake of being expensive. You can charge quite a bit for precious metals in a good weave. In fact, underselling yourself is bad for business! Sure, I could make a bracelet with some 75 rings and that'd cost me like 30 cents or so in aluminum rings, but who's going to buy a bracelet for 50 cents? Cheap piece of garbage is gonna break as soon as it comes out of the package! Put the price at $5, or $10? Now you've got a fairly inexpensive piece of woven metal jewelry! Plus there's labor. If it takes you 3 hours to weave a very nice bracelet, and costs $2 in materials, and you charge $10 for the finished piece... then you're paying yourself $2.66 per hour. Minimum wage here is like $7.50, think about it...
I'm getting distracted though. Get yourselves some gloves, for real. I use cheap gardening gloves when I'm coiling wire, but I've seen one person who'd taken welding gloves and stamped an inch long aluminum sheet over the thumb, because he was coiling stainless steel and that will murder your hands. And I don't know how you're doing it, but the nail shouldn't be touching the wire anyways...