Since you are at 30-06's and 12 gauge stage(ones first three long guns should be a 22LR, a 12 Gauge, and a 30-06) I would recommend the 375 H&H as your biggest "jump". It is a classic (94 years old), it is semi-friendly without hard work, some consider it the very bottom rung of the "big bore club", you can reach long with it, and for NA game it is a thumper, probably my favorite for elk. The cartridges aren't overwhelming to look at, but they sure do the job (300 grain TSXat 2,450 fps and you can eat right up to the hole).