All the small/medium fast caliber with a tense trajectory are a good choice.
The 6 mm are excellent: 243 Win, 6XC, 6 mm Rem, 6mm Freres and 240 Wby.
Good are also the 0.25, for instance the 25-06 and the 257 Wby even though a little hypertrophic.
The 270 Win and the stronger 270 Wby.
The 7 mm are a good choice as well, the 7-08 is considered a perfect caliber for mountain hunt, precise end lethal, the same for the 7×64 with a proper ammo (120gr.)
For long range shooting the 7 mm magnum and all the 300 mag can support shot between 400 and 500 mts even if they are overabundant and with a strong recoil.
The best ammo are in copper and we suggest the new monolithic construction ones.