You gunsmith gave you a good recomendation. The 300 win mag is a fine round as long as you are capable of shooting it well. If recoil is not an issue it will serve you well.
One can drop down to 150 & 165's for antelope and deer and go up to the 180 & 200's for elk if desired. If you are on a limited budget it is an excellent choice. Others good one gun rounds would be the 7 Rem mag, and the 300 weatherby and of course the 30-06 and 270.. The only drawback is for the 270 I'd want to keep shots 200 yards and under for elk to assure good clean kills.