I know you said you were trying to stay away from plastic, but you also said you would like to reuse/recycle. I use 1/2 gallon
milk cartons to winter sow the
honey locust trees that Dan Boone sent me. They will be planted out this spring and they aren't even up yet.
Since you're using them for saplings and not seedlings, I would suggest gallon milk jugs with the top cut off.
I have a battery operated soldering iron to make drainage holes in plastic. For paper cartons, I use an ice pick.