You can use vinegar/water solution or bleach/water (1/10 ratio). I actually don't clean branches, I prefer to leave the bark and stuff on for added grip and I like the natural look. I usually pick poplar branches from my yard that have fallen recently or cut live ones off.
Agreed branches can be cleaned that way, but i prefer not. Unless theyre near farms or anywhere else similar I wouldn't worry. For plants I clean with a soapy vinegar mix. Doesn't really matter which soap, just rinse well
My main concern is picking rocks and branches that have pesticides on them. I can just pick these things up in my apartment complex but I'm almost certain they are carrying pesticides since we pay a monthly pest control fee. I could always buy some rocks from home depot or try finding branches somewhere else, but if they're right outside my door then how could I say no to that haha