I split slats out, then plane the sides straight. I have a jointer, but prefer to knock down the inner nodes with a draw-knife, then I put a cheap block plane I have upside down in a vise and pull the bamboo through it to do most of the thinning. Then I go to the sander to smooth, level, and finish it.
The little green stuff I have used, i just cut, split into 2" slats and dried it in a dry place, in the sun, off the ground. I live in Utah, so drying things is easy. ;-)
I would cut the largest diameter available, unless it has problems like nodes every 3 inches or something.