A standard weight 260rem, with a good recoil pad would be close to ideal.
Not famaliar with the .260 REM personally, but the external/terminal ballistics look good and so does the free recoil generated.
.250 Savage is sweet but ammos a problem these days.
The .243WIN should get it done, there's lots of premium bullets in this caliber to make a good showing from gophers to Bucks! Id say try to stay 90-100grs if recoil is a problem. My only .243 was a Remington 7400 in 1983. Recoil was light but Rifle was heavy!
One you hit 120-130grs you start to get some noticeable recoil(youths, petite ladies, elderly etc) on many Hi velocity rounds in sporter weight Rifles.
The .30-30 you mentions may hurt his shoulder being frail , if its an 1894 ,I find they climb and slap the cheek a little from the Drop at the comb/heel of the stock. Hard butt plates don't help either. This is what makes their unmatched, quick shouldering abilities.
I forgot to mention check out the variuos recoil calculators on line. Alot have generic bullet weight/charge combinationa along with Rifle weights.
If you know the total weight of the firearm you can see the different recoil energies/recoil velocities.
It will give you a good comparison between cartridges. I just checked one out and the little 250 Savage with the classic 117 factory load for deer, only generates 7.7 ft lbs recoil in a Rifle scope combination weighting in at 8 lbs total. I knew it was a sweet shooter!