Newest addition to my collection

Just got this in the mail a couple of days ago. Snagged iot for what i figured was a good price and had to have it. The rubber is starting to deteriorate some, any one have any thoughts on how to deal with it?

There is not really anything that can be done. Once rubber starts to degrade the process cannot be reversed. Rubber naturally deteriorates from being exposed to the air. Limit how much the mask is handled and be happy with what you have is about the only advice I can give. Be wary of applying chemicals and lotions as many will make the mask look good for a short amount of time but actually accelerate the deterioration process.

Would it be better to store it in the pouch or out?

I think it would be best to keep it out of the pouch and if you could put something inside to help keep its natural shape that would be best. Also, that way you can see the mask and enjoy it. If all you want to do is preserve the mask for the future then you should find some way to store it in a vacuum...

Any tips on the best way to display the mask so it keeps it nateral shape?

I have used a large round styrofoam ball in my WWII child's mask I think it was about a 5 or 6 inch diameter. It has a fairly good fit to the smaller face size. I left the original plastic wrap on it to avoid any problems with the foam.
You could use a stryofoam head but I would avoid hanging the mask off it as that will introduce a lot of strain on the head piece straps.