Agree with Drago
But it might be an idea to keep him in his old cage after you move until you've worked out what will fit best in your new place and where. Although they can be a bit stressed for the first week or two at the change of environment at least the cage will smell familiar so don't clean anything before you move. I bagged up the substrate and toys etc, moved our hammy in his pet carrier on the day then reassembled it all when we got here. The cage got put in the quietest room while we unpacked and he went in it. Then it ended up being moved to somewhere more suitable (which didn't help but he was ok with it). Ideally put the cage where you plan to keep it for a while when you move into the new place.
But - as Drago says, if it is a big change anyway then moving into a new cage won't make a big difference, especially if you re-use his substrate. I think I would wait though, because setting up a new cage and getting it right can be a bit time consuming and a fiddle and maybe not the best thing to be doing when you are upheaved and unpacking etc!
Either way would be ok as long as you don't have to keep moving his cage around from room to room after moving, so maybe plan it a bit before you move in. eg where the old cage would go/fit, where a new cage would go/fit.
I ended up with Charlie's cage on top of a load of filing boxes as a temporary measure and then didn't want to upheave him again so it stayed on top of the filing boxes the whole time he was still with us!