I'm not sure on if there are any you should avoid. Once you strip the bark, you can bake them a low temp at or soak them before putting them in. in.https://www.chameleonforums.com/bake-not-56349/
This is an old thread that I started when I was just getting started.
Not sure if you have access to any grapevines where you live, but if you do, vine branches work great. Soak them overnight in water so that they become bendable without breaking. I live in wine country so when pruning season comes around I'll be stocking up again. They are free and work great.
Don't use pine, but I think anything else is fine. You don't want anything with sap, because that's a mess (especially in the oven... I know from experience. Although the house smells fantastic!) and apparently pine sap can be harmful to reptiles.
I did not read the bake or not to bake thread, but I have a question... why NOT bake? Baking dries it out thoroughly and prevents molding, it kills a lot of what might "come in" with it, because you don't know what was sitting ( or pooping ) on the branch before you brought it in, and it would suck to bring something in unintentionally.
If you get something like willow, or elm it's a softer type of wood and you could probably bend and form that pretty easily while it's wet/just cut.