i use sticky-tac to hold down the bottoms of my prints! it’s almost like chewed gum (gross description sorry...) but it doesn’t peel off paint and sticks pretty well! i dont use it to solely put up my posters as it’s usually not strong enough to hold the full weight of thicker poster paper but it works perfect for keeping them from peeling up ☺️
I have a ton of pictures hanging in my apartment by sticky tacky right now- as long as its not too humid where you are, there should be no damage to the posters or the walls. If not, I also have two posters hanging in my room in frames. Amazon sells two-packs of poster frames for like $25 that are super easy to hang.