I've tried cork, felt, and leather. I like and use leather almost entirely. I've gotten some bad felt belts from Supergrit and that put me off a bit. These belts were blue, would melt onto the surface of whatever I would try to polish, and had a coarse abrasiveness to them that defeated the purpose of trying to polish with them. While I have one good felt belt, it's only 1/2 X 42. I leave it clean and only use it for deburring on a rare occasion.
Cork needs to be broken in which is not that difficult. Also, the only cork belts I've used come preloaded with abrasive. I'm not a fan of this as I like to load my own abrasives. There may be some plain ones without, but I haven't really shopped around to see. My corks are old, with the original abrasive gone. I have one loaded with Boron Carbide and the other loaded with Cro.
Leather is my favorite. It holds compound better than anything else and grabs the blade edge better than anything else. Leather will stretch over time or if left on the machine while not in use. I have a Kalamazoo 1x42, Craftsman 2x42, and Viel 1x42. The Viel, probably not unlike your 1x32, does not have adjustable tension. But I've never had problems with flop on a loose belt as long as I sharpen between the platen and the top wheel. If the belt gets too loose though, it will track off of the wheels while polishing.