I've never ever heard apposite used, nor have I ever read it in any book or newspaper. I'd avoid it - even though it appears to be a real word, it's very uncommonly used. Appropriate, proper, and suitable? Suitable is typically used to describe something that's "good enough" without going further. "The neighbors found a suitable solution to their dispute". Neither appropriate nor proper really sound right in that sentence. Appropriate and proper are more/less synonyms meaning the right decision. "What's the appropriate / proper thing to do in this situation?" Suitable wouldn't be used in that sentence.