What are the nuances between each? For general use in most cases can they be substituted for 準備します?
None of these words can substitute for 準備する. They are not synonyms.
整う means for a bunch of things to come together to make a cohesive whole, or everything's in its right place. 準備が整った，夕食の用意が整った
I've never seen 設ける used to mean prepare, though. I did find 一席を設ける though, "to plan a party". But moukeru usually means to establish.
備える means to keep to do something or keep something somewhere in preparation for something else. Commonly seen as にそなえて. 台風に備えて懐中電灯を買う, in prep for the typhoon, buy a flashlight.
Only そなえる really has a meaning of "prepare", in my personal opinion.