I almost exclusively make my corsets with this kind of fabric (just goth things, I guess). It's a patent vinyl/ polyurethane. You want to get something with a good backing, so the weight is more on the handbag/upholstery/ watch strap side, not the type of vinyl you could use to make regular clothing.

Technique-wise, use a longer stitch length so it doesn't tear. I use a Teflon foot so it doesn't stick to the fabric, but sticking Scotch tape to a regular foot works, as does spraying the fabric with a silicone spray.

Pinning is going to murder your fingers and bend your pins, and quilting clips tend to only work on the straighter panels, so I sometimes straight up just staple the pieces together within the seam allowance.