Haven't used a 7mm but a .30-06. For smaller and medium sized plains game a 7x57 will do fine. Similar to any 'deer' rifle. I would probably use a good premium expanding bullet in 150 gr to 160 gr range.

I remember reading an article years ago about 'wives' using loaded down - for recoil reasons - 7x57mm rifles and they killed well. They used a lighter 135 gr bullet which may have worked fine due to the lower velocities.

The 6.5mm and 7mm are 'classic' African calibres for this so I wouldn't expect any problems with proper bullet placement.