I have a .270. I want something a little bigger.
Well.....you don't need it but you sound like a 30/06 candidate.
As my good friend Bob pointed out, you are good with the 270 with good bullets; that said, it was not the answer I was looking for thirty years ago either as I tried most cartridges and many rifles commercially available. So if you want another rifle... but, within 300 yds. as you specified, it is not worth getting a magnum of any stripe. IMO, from 400 yds. and out and for heavy-for-caliber bullets they have their place for big game.
I would focus on good glass first -- bino's (7x-10x) that you really hunt with; second, a good scope (3-9x, 2.5-8x, 3.5-10 etc.) and a solid rings/base combo of which there are many. Then boots and finally good, layered garments and pack.
And so on. And welcome.
