The 7mm-08 has tons of supporters..for good reason...it is a stellar caliber for kids and women...the 243 is amazing as well and that was my first caliber center fire rifle from my Great Grandfather. I now own a few different guns but one I've really grown fond of with light recoil is the .260...
You might consider the 260 Remington or the 284 Winchester....the 284 has a little recoil for my shoulder but much less than the 7mm mag and it is almost traveling the same velocity. The 260 is on the light side but it it moving pretty good also look at the 25-06. Good luck. With 400 yards...
Here is a photo of my husband's bull this last year... he shot him in Sept 2016...he shoots a 7mm mag but we switched from bergers to 150 grain accubond lrs going about 3007 fps...
This bull dropped when shot at 50 yards in one shot...right where he stood. I'll have to post some more results...
This may be a little late to address this on the forum but here is my hand load data I'm used out of my gun:
I was pushing a .308 210 Berger VLD right in the 2750 fps window where my rifle seemed to really stack them tight... I wasn't able to get that good of down range forgiveness and...