Welcome ohpedro. It's always nice to see an introduction with a little bit more depth than usual.
I'm sure you'll receive lots of advice & hopefully some of it will be of use.
The only air rifles I personally own are dart projectors, but IMO modern air rifles are surprisingly powerful & accurate. I have observed the effectiveness of modern air rifles several times in the last few years & have consistently been left in awe at their accuracy & effectiveness. In some parts of the world folks now also hunt big game with large caliber "slug guns". You may be surprised at how effective the modern air rifles would be on foxes around the chook sheds. But you can never have too much gun so apply for as many categories as you can whilst you are at it.
Look forward to seeing more posts on your progress.
All the best.
Sharkey