I have tried all sorts. Based on what I know about sharpening (working through the grits, etc) I bought a selection of different grits and types initially to see what works best. What I have found works for me are just standard cheap belts. I used an 80 grit belt to reprofile all the tools to fit the pro edges jigs initially, then worked through the grits (120, 180, 240) to get a nice sharp edge on each tool.
What I find now is that I just leave a 180 grit belt on the machine while I'm turning and give the tools a quick once over with this as the edge dulls. This gives a nice sharp functional edge every time and super quick.
I might change for a finer grit belt if I need a super sharp edge for a finishing cut in some tricky timber, but for most of my everyday turning the 180 grit belt lives on the machine.
I've tried ceramic and trizact but always revert back to aluminium oxide - cheaper and they last well when I use them as described above.