Ammo: Same Brand, Same Bullet, Every Shot 
With the money you save by using a bore sight, you can now use to purchase higher grade ammo (perhaps Hornady). If you’re really trying to get dialed in like a sniper, match grade ammo will make a difference.
Whether you upgrade your ammo or not, it’s imperative that you sight in with the same exact ammo you plan to hunt with.
Even more importantly: Don’t just grab an assortment of old leftover rounds while you are sighting in. Different weights and manufactures (even different lines within a single manufacturer) will all fly a little differently.
The key is that you minimize variables, especially when sighting in your rifle. Lots of folks want to minimize their costs by using remnant ammo. Bad idea.
If you sight in with Remington Core-Lokt 150 grain ammo, go buy a bunch of it. Shoot only that ammo, all hunting season long.