Making jump rings is easy to do. You can make them in any size you wish - with any type of wire you choose. The size of the jump ring depends on the size of what you are winding it around. Jump rings are in-expensive and somewhat easy to find. In my town there is not alot of options so I started making my own.
Here I have used BBQ skewers for my jump rings. I am trying to find something smaller than these items to make super-tiny jump rings.
I wind the wire around the BBQ skewer.
Then remove the coiled wire and snip ( wear goggles or close your eyes real tight LOL )
genlty bend the wire to form a proper ring.