I would highly recommend a 7mm mag, or 7mmRUM for those distances. It won't be overkill unless you make a bad shot. A 100-yard shot square into the pelvic girdle with a structurally weak bulletwill leave you with 1/2 of a deer.

I use 300 wby and it's fine. I'm comfortable at any range out to 400. 7mm offers similar ballistics.