I use a leather needle to sew leather, vinyl, pleather, laminated cotton, oilcloth, foiled fabrics, and anything with a similar coating. A leather needle (in, as with all needles, the appropriate weight) is all you need to use to make sewing any leather-like material work without any unwanted sticking.
Because the problem is not the vinyl sticking to the machine bed or the presser foot or the needle, the problem is that the holes made by a standard needle are so small they don't allow the thread to move how it needs to. Leather machine needles (and glover's needles for hand sewing) have broad tips that cut tiny slits in the material, which makes enough room for the thread to move freely. I have been using leather needles for machine sewing leather-like materials with no problem for nearly 20 years and I have never needed to change anything else about my machine.
But.
I am still very bad at designing purses.
See, in an effort to remind myself how easily vinyl sews with the correct needle, I dug through my small pieces storage and came up with some vinyl remnants that have been in the stash for a least ten years each (and are still stable, instead of disintegrating like some early 2000s vinyls have) and then gathered other things that seemed to coordinate with them and ended up with this pile of stuff
which, over the course of a few days, I turned into...this
Don't worry, there are many close ups of the bad design decisions under the cut