The Cooper sounds like a fine rifle and it's what you want, so get that.
As for cartridge/caliber: based on what you described, the .25-06 Rem would be perfect. Good power. Very flat shooting. Mild'ish recoil. Deadly on deer and black bears. 115 Nosler Partition will be your go-to bullet here. Good expansion out to 400 yards and great penetration, even on close shots where impact speed is high.
Next choice(s) would be the .260 Rem or 7mm-08 Rem. Again, good power, manageable recoil, and factory ammo available. Flat'ish shooting.
As for cartridge/caliber: based on what you described, the .25-06 Rem would be perfect. Good power. Very flat shooting. Mild'ish recoil. Deadly on deer and black bears. 115 Nosler Partition will be your go-to bullet here. Good expansion out to 400 yards and great penetration, even on close shots where impact speed is high.
Next choice(s) would be the .260 Rem or 7mm-08 Rem. Again, good power, manageable recoil, and factory ammo available. Flat'ish shooting.