I try not to flatpack them as when the box folds it creates a crease down the edges (that might just be my ocd and fussyness though!) but when I carry them I place them into a cardboard box of similar size so it doesn’t move around and fits in my bag perfectly :). I use the boxes that my pops are usually delivered in if that’s of any help!
I’ve tried the Sharpie paint pens but I’m a bit weary of them. Personally I’d suggest Posca, but it also depends on the person who’s signing if they hold it correctly. I often have mine signed in normal black sharpie as I’m usually in a rushed situation and there’s no time to ask them to change. At a convention as it’s a calmer situ and they can sit there and do it carefully, I’d maybe try them then? I’d definitely watch YouTube videos though on how to get the pen ready for usage :)
Also, after I get my pop signed I place it into a clear acid-free POP box so the auto is protected too!