I'm kinda late to the post & see a lot has been covered. I was lucky enough to have gotten into the "sheep game" way back in 1998 & international sheep/goat hunts in 2007. The international travel experience is hard to beat for the price. There is extra expense getting them back home & travel.
Ibex are cool animals you have to earn on hunts & have a wide diversity of places to hunt. Mountains, deserts & even a Greek island. Every one I've been on has been a great adventure.
The tar & chamois of New Zealand is a great place to start. Just be sure to tell your outfitter exactly what you want from the hunt. I spent 5 days hunting out of a tent for both of my trophies.
Spanish ibex are great hunts & easy to take wives along. Most are affordable as long as you don't want to hunt the upper medal class animals.
The little chamois are fun to hunt & a great value. Don't overlook this little mountain goat. I just returned from Romania and a very challenging Carpathian chamois hunt. I know they don't have the same "cool" factor as ibex but are still a good adventure.
International sheep hunts can vary a lot in prices. Big difference between a Kyrgistan Hume(MP) hunt ($20-30k) and a Mongolian Altai hunt ($150-350k). European mouflon can be found all over & are very reasonable in price but most often are not a difficult hunt.
Tur are one of my favorite animals to hunt! Azerbaijan is closed right now but the Eastern (Dagestan) tur can still be hunted in Russia, along with the Western and mid-Caucasian tur. I've known several hunters that have traveled to Russia the past couple years without troubles. I have an ibex trip scheduled for 2025.