2 Budgies, 3 Cockatiels, 6 GCC'S, 2 Crimson Bellie Conures, 9 Sun Conures, 2 Major Mitchells, 12 Eclectus parrots of various ages, 2 BF Amazons, 2 Hahn's Macaw's, 1 Red Tail Black Too
I did some experiments and they seem to prefer to roost on an apple branch which is about the same diameter as your finger, if I remove those the next choice are hanging rope circles.
I think the guidance (in so far as anything online is actually true...) is 75% foot wrap, I just tested it on my java (which they don't like because its slippy) and it comes out as roughly 3/4 inch or 2cm diameter.
We have about 3 or 4 different thicknesses, he always chooses the biggest one(possibly only because it's the highest, but yea I wouldn't say anything too thin. Don't forget as well that they'll usually chew thru any perch, so nice thick hardwood is good.
What country are you? Aus has some really good suppliers that I can pass you on to