I don’t know the price at the moment but here I’m using Turtle Skin.
Sufficient to handle thorny bushes although it only has puncture resistant on the palm.
You mentioned budget options so I thought I would pitch in.
For an inexpensive option I have used Harbor Freight welding gloves ($4-$5), the extended gauntlet is useful for avoiding thorns but not puncture proof.
Also, my favorite, a wrap or two of dense weave duct tape (Nashua 357) on any glove is really helpful. My brush handling gloves at this point seem to be almost entirely duct tape and years old, just apply more when abraded or needed. Started this when I was having a hard time letting go of a favorite pair of gloves and now often wrap the new heavy work gloves from the start.
Cut resistant (woven Kevlar) is definitely not puncture resistant. Any point narrow enough to get between fibers of the weave and spread them apart will poke you.
Cut resistant material is proof against slicing, not stabbing or thorns.
You can find cut resistant gloves marketed as “Chef’s gloves”
I’m an ironworker and those gloves just won’t quit. I usually go through leather driver’s gloves in a week or two, these have lasted over 6 weeks now and still don’t have a puncture or slice all the way through. Toughest gloves I have ever had!