Factoid: the abbreviated / over-simplified explanation of Grendel vs ARC
6.5 Grendel has been an established cartridge for +15 years with Alexander Arms trademarking the name “Grendel”. During this time it has been wildcatted (necked down) to a 6mm, known as 6mmAR, and also 22 AR / 22 Grendel. Neither of these two wildcats based on the 6.5 Grendel were SAAMI Certified. Hornady being the marketing machine that it is simply copied these cartridges (minor tweak to case), renamed them as if they were their proprietary development, and submitted them SAAMI Certified as 6 ARC and 22 ARC. Ta Da…
Based on what you have detailed as criteria and budget, and ignoring my personal preferences / bias, my recommendation are:
1) Cartridge: .223 Remington
> least expensive factory ammo and readily available everywhere.
> factory rifles are chambered in this cartridge by every manufacturer. No need for custom barrel or gunsmith for this cartridge.
> easy to reload with wide selection of reloading components (bullets, powder, brass, dies, etc).
2) Rifle: New Factory or Used Rifle with a medium weight barrel profile (20”-24”)
> Let go of Mossberg fantasy… they make a decent shotgun, but their rifles are not their strength. You need to focus on performance, and not get seduced by exterior appearance or brand loyalty. Sorry
> rifles to consider Bergara, Howa 1500, Savage, Ruger American Gen 2, and Tikka. I would look hard at Bergara, a lot of rifle for the money and becoming an industry sweetheart. For a factory rifle Tikka is superior in machining (smoothest factory action and accurate) and would be a stretch goal, but money well spent.
3) Optics:
There are several newer scope manufacturers, such as Arken, that deliver a tremendous value at an extremely reasonable price (5x25 for $500). Yes, most of these budget scopes are made in China. The secret is out that many of the scopes sold by different companies are actually made in same Chinese factory with only difference being exterior cosmetics. Some offer a premium model that features Japanese manufactured glass lenses. Do your research and watch some YouTube comparison videos to identify the right scope for you.
Good Lucky and Happy Shooting.