What would a suit that allows you to travel to a dimension made out of Anti-matter be made out of? It couldn't be matter, nor could it be anti-matter. What's left? Electro matter? Matter's badass grandpa?

In a shadow dimension you would probably have to devise some form of vehicle that's capable of permanent flight, as you literally could not touch anything there. It wouldn't work in an antimatter dimension because the gasses would be antimatter as well. 

In a fuckall dimension it's one of those things that falls solely to theory and GM moderation, if the physics there make you die or worse you'd need some kind of contraption that allows you to defy nonsense physics. Which is even more nonsense than a dimension of nonsense.