I know you say you don't like recoil but a 20ga shotgun is on the higher end of 'rifle' recoil at around 20-25lbs/ft.
https://chuckhawks.com/shotgun_recoil_table.htmA 30-06 is going to be around 20lbs/ft of recoil, 308 around 16-18lb/ft, and 30-30 around 10-12lb/ft.
https://www.chuckhawks.com/recoil_table.htmAnother consideration is that 30WCF rifles tend to be predominantly lever action, (more expensive, and generally less accurate than a bolt gun though how much that matters at 100 is debatable).
A savage 10/110 (not even the axis series) could be found with a decent scope combo (Apex hunter package I believe) for around the same price. And any of the above calibers would offer more versatility, but possibly less cool factor, of the lever 30-30.
If you really want to stay that low on recoil but want the capability of a full rifle cartridge the 7mm-08 is a great choice. Basically a necked down 308 to 7mm, achieves flatter trajectory, and minimal difference in game effectiveness and recoils not much more than the 30WCF, and notably less than even the 308. Factory ammo is generally very good in normal times.
We called them "girl guns" or "women's guns" around here, not as a derogatory term, but because they were very well suited to recoil sensitive individuals, those of smaller stature, or just those that didn't want 308, and offered fantastic ballistics with almost no compromise.
