The thickest sized ones I have found were Pereskia grandiflora...they also have an upright growth pattern. The least vine like when they get large. Not sure about rate of growth, but they may better support grafts. I heard pereskiopsis is better for speed of graft growth, but I haven't read anything about that.
Of course I see this now after ordering some others! I got Pereskia lychnidiflora (the one i bought hopefully might be a misidentified quiabentia sp.!) , pereskia bleo which also seem to be thicker stemed and upward growing.
This is also part of my own pseudo-experiment to test out different cacti rootstock for columnar/larger cacti.