6.5 creedmoor or 270. Low cost ammo with a huge variety of loads. If buying bulk plinking ammo is a priority, creedmoor. Honorable mention to 308. Other calibers will do the same thing with increased cost or decreased selection of factory ammo.
Target 7.5 lbs for gun and scope if hiking, towards 8.5 lbs if mostly stand hunting.
Ruger American is a great entry level rifle, you can spend more if you want to, but it won't impact your ability to get game. Browning xbolt is my preference. Great stock ergos, accurate, great removable magazine, tang safety, tons of options for caliber, stock material, and metal finish.
2-7x scope is perfect, maybe 3-9 as they're more common. I've been happy with the VX freedoms I recently bought. Fullfield II is another option, but had a bad one on a 300wm. Not sure if the NIB scope was bad or the 300 killed it. My other scope recommendations are either discontinued or lot more money. Zeiss Conquest, VX2, VX5 2-10 or 3-15, Zeiss V4 4-16, Z5 2.5-12. Haven't seen any difference in my ability to harvest game with a Redfield 2-7 vs the V4 or Z5.
Most important part of the mounts is making sure the scope isn't bound up. 1 piece DNZ make the initial setup just a little bit easier and haven't had to lap a set yet. Lightweight too. Usually a low height, maybe medium on a rifle with a higher comb like a kimber.