Lots of good ammo choices out there.
Lots of factory loads available. Winchester has some excellent hunting rounds, as does Remington, and Federal. I'm sure there are a dozen manufacturers that make similar hunting rounds suitable for Mule Deer.
Winchester makes one I'm fond of that
you can see here. That's a ballistic silvertip in 180 Gr.
If you need more power. Winchester makes an
excellent round for larger game. That round is intended for Elk and larger to just this side of Water Buffalo and Elephant. I don't believe I'd try and annoy one of those critters with a 30.06, but you may be a braver man than I am. Supposedly it would be suitable for large brown bear, including Grizzly. Again, I don't know about that, I've never hunted them. Not sure I want to try either.
Remington makes good rounds as well.
Federal also makes some great ones. I'm just partial to Winchester rounds for my rifle. I also have a 30.06 but use the PSP rounds for local game in Georgia. The Winchesters shoot very good groups in my rifle, so I tend to stick with them.
Just look for rounds that are intended for your target, and you can search for hunting stories online, or even call up to the guides in Wyoming, and see what they suggest.
Remember, in Wyoming, you have lots of open shooting. So you should be ready