Pronghorns are my favorite and the animal I have taken the most of.
Elk hunting is wonderful, mule deer are ok, whitetails are boring, roe deer are the my tops favorite of all deer species.
I have hunted aoudad in New Mexico unsuccessfully in the 1990's and ibex unsuccessfully in Turkey in 2000 with local Turks.
if I could afford anything I would do as many sheep and goat hunts as time permits every year. I'd apply for as many pronghorns, and buy as many land owner tags as I can humanly do, and I'd hunt elk and red stags every year.
Red deer are wonderful because of their vocalizations. I have only shot red deer females, as the stag prices were more than I could afford.
Pigs are fun, bears are fun, and predators are fun.
Beyond that nothing else is as interesting.