If you're going to make your rings, just go to the local Home Depot, Lowes, or Canadian Equivalent, and pick up some galvanized steel, preferably some 16-18g if you can. Then you can use a metal rod with or without a hand crank - if you get a rod that has two 90 degree angles in it, it makes a perfect crank from which you can wind the rings. They generally call these "mandrels" when they have a hand crank, I believe. TRL sells mandrels and rods in a TON of different sizes and styles, with notches, holes, tapered tips to fit into electric drill bits, and hand cranks. You can build a small spinning rack if you've got a 2x4, saw, and drill. All you need is a U shape, and then put the mandrel through to make a U shape.
If you're going to buy rings, go aluminum. It's 1/3 the weight of steel, so you're buying 3x per ounce, and it's cheaper than steel so you're getting more like 3.5x-4x per dollar (or Canadian Equivalent, whatever money it is you use...). Saw cut rings are much much nicer, but machine cut is cheaper, and if you're just learning how to weave you should probably go cheap and experiment a bit.
Galvy is available in hardware stores, as it's fencing wire and often used for electric fencing. Aluminum is also available, but this is dirty aluminum and will rub black against skin or clothing. Don't get it. Most packages are simple spools, but some have plastic wrap over them, so you can easily touch your finger to it and it will turn immediately black.
Rods are available in hardware stores as well, you might check the concrete department, as they're often used as support rods when people are pouring a concrete foundation for a deck or whatever. About 3-4 feet long in a small variety of materials, usually $3-4 for a rod and they come in a variety of sizes. TRL sells a lot more rods with a lot more precision and some chainmail specific additions, such as a notch in the end to put the wire through to make winding easier, labeled size, and a tapered end that will fit into an electric drill for easy spinning. TRL also sells a TON of very specific sizes in all ranges, from 1/2 and maybe 3/4 down to like 1/32 or maybe even 1/64, often available in package deals as "Jeweler's Rods" or "Armorsmith's Rods" for a given size range.
I personally started with PVC pipe. 1/2" pipe barely fit into my drill head, and after every winding I would have to cut off the tip because the drill's closure would mangle the pipe and ruin it, but I could wind up about 500 rings at a time easily and use that pipe a solid 50 times if I was smart. Used a drill and a small bit to punch a hole through, slip the wire through the hole, and that made winding a LOT easier.
For size, I generally recommend 18g 1/4" as a starter. It's a solid size, makes a variety of weaves easily, is big enough that you won't get frustrated with tiny sizes, and is small enough that it doesn't look cumbersome. In Euro 4-1 it makes a weave that's loose enough to show off the individual rings yet tight enough to hold its composure. I personally don't go any thicker, 16g looks bulky to me, but I'm making jewelry so I'm not going for thickness. 20g is pretty fun as well, allows for tighter and more flexible weaves, but you may find yourself needing some chain nose pliers instead of traditional wide nose.
As always, consult the youtubes. You're not the first to ask about this and I'm not the first to answer.