My wife and I both shoot 7mm-08 and are very happy with it. It has excellent performance and good availability, and a wide range of bullets and suitable loads. (I went with a 150gr round.)
This started by my buying her a Weatherby Vanguard Camilla, a rifle with a stock specifically made for women.
https://weatherby.com/store/vanguard-camilla/ It's a great rifle and in this caliber, shoots soft but hits hard. She fell in love with it.
I had been shooting 30-06 until then, but I fell in love with the round too and decided to try it myself. I picked up a budget Savage XP Hunter in it in a carbine length and that's been my go-to for the past 3-4 years.
I'm not sure about the ammo-harder-to-find detail. I feel like a lot of ammo is still in that category if it isn't shipped by the pallet (e.g. 9mm handgun). Right now, Sportsman's Warehouse and Midway both have several options available. YMMV, but for me, this thing is the sweet spot.