Question?

I am looking for a long range rifle, and I think that I have narrowed it down to the 22-250 and the 300 Win ultra mag. My intentions are to mainly punch paper, but I am trying to get into varmint hunting. With the 300 I can use accelerator bullets, but still have the versitility to up the grain and moose hunt with it. The 22-250 is a well known caliber for varmints, but it is limited as far as anything other than paper punching. I hope you can shed some insight on this for me.