Andy if you want the best plywood, you should go for Lloyds approved stuff. If you want really good stuff, go for marine ply. and if you want something that will do the job, and is going to be covered, go for external ply. As with everything , it's all available at a price.
I've used Edens for the ply on the current build. I thought they were reasonable.
http://www.edens.co.uk/gfx/ul/files/Page06_1.pdf
If your going for a glued sandwich wall, I would think 4mm sould be fine as long as you have framing where you need strength. If you think of a panel door, the ply is not thick.
If you ever strip a caravan down, you'll see the walls are very thin battens,insulation, and super thin ply (3mm?).
Good to see you making a start