Many people use random sticks they have found outside. Generally avoid sticks with mold or fungus growth, sticks that are rotting, sticks with sap, sticks with sharp edges, and any thing with oily toxic wood.
Many people also feel it is a good idea to sterilize the branches. I personally boil for 20 minutes, some bake in the oven, steam, soak in vinegar, chlorox, etc...
Sterilizing outdoor items is tricky and there are many different ways to do it, and more than a few here don't do it at all.
As far as humidity, lots of live plants, covering 2 to 3 sides with some form of barrier both work. There are literally hundreds of in depth discussions on the subject here, I suggest doing a search.