I'd suggest what I am going to do with my new rifle . . . as a part of breaking in the barrel and comparing different store bought ammo in it, I am shooting three different ammo to see if the gun likes one or the other. I will use Winchester X in 150 gr, Federal Premium NP in 180 grf, and Hornady 168gr A-Max. Kind of pricey for "breaking in", but I'm also seeing what my gun likes. It DOES make a difference.
I'm not saying you have to go out and buy three or four boxes of premium ammo, but try at least two in different weights.
Something else that is always in the back of my mind is to match the cal. gun with the ammo manufacturer. A 270, 30-30 and .308 are all rounds developped by Winchester so I might lean towards them for ammo.
On the othert hand, the 7mm, 25-06, and 22-250 were Reminbton creations. See what I mean?
If nothing else, you sure will get some practice in!!