Oh deer! I'm quite partial to these guys personally, so these are going to be some tough picks.
Personally I think the Red Deer is the most likely one to be added to the game since we already have statues for it. Honestly I think it would be a really nice species to have in PZ and it could wrap up our roster of European animals pretty nicely. Like the Alpine Ibex, it's one of Europe's more iconic animals.
I think the American Elk is a pretty important one to include as well. They're very big and impressive, second only to the Moose, so I think that would make them a great addition to the game. If I could pick a particular subspecies I'd choose the Rocky Mountain Elk since it has the biggest antlers and it could make for a really cool interspecies enrichment with the American Bison and Pronghorn Antelope. If this species was added I could finally do a proper Yellowstone National Park styled habitat with those three species living together.
While the White-Tailed Deer is common all over North America and I see them out in my backyard all the time, I'm actually more partial to its western cousin, the Mule Deer. They're found across western North America and I think they would be a great addition to our North American sections of our zoos. Their forked antlers are really cool looking imo and they have a very unique way of running called stotting. They'd also make for a great interspecies enrichment with the Bison, Pronghorn, and possibly the American Elk if it were to be added, which would be really cool as well, since they all live together in many parts of western North America.
Another spotted deer species would be great too, just to give us some variety. I think the Sika Deer would be a really good fit for the Asian sections in our zoos, although it does look a bit like a smaller Red Deer in a way which might make it a less popular choice. Therefore, my second choice for a new spotted deer species would be the Chital, or as we call it here in the United States, the Axis Deer. I think it would go together pretty well with our other Indian animals in the game.
A smaller deer species like the Pudu, Muntjac, or Tufted Deer would be really cool as well to show the sheer diversity in size that deer species can have. The Muntjac, like the Chital, would be great if you wanted to do a dedicated India section in your zoo, so it would be my preferred small deer species personally.
I do like the Père David’s Deer despite my unfamiliarity with it. It would definitely be a unique choice, but not my first one.