The gun part is pretty easy. Ruger American is hard to beat bang for buck. It's stupid precise for its price point. My Ruger American Predator shoots 99% as well as my $7,000 precision rig.

The optic is the tough part. There's a sweet spot for glass that's way better than the cheapo stuff, but does 90% of the pricey stuff. Look at product lines, not necessarily brands. Vortex, for instance, has 4 main product lines (Crossfire, Diamondback, Viper, and Razor), with the lowest-end being absolute dogs hit in any kind of low-light situation, and the top end being stupidly expensive for the limited benefit over the mid-tier stuff. In that brand, I'd recommend a Diamondback for a budget gun, though something like a Leupold VX-2 or 3 may get you better glass.

But my goto secret scope is to try and find a used Cabela's Instinct riflescope. Lots of people look at store-branded stuff as garbage, but Cabelas (prior to the Bass Pro buyout) had some higher-end stuff. The Instinct Scopes were actually rebranded Meopta scopes, and you can sometimes find them online or at a flea market bin for under a hundred bucks, while the glass is the same Schott crystal you'll find in $2000 scopes.

Another Cabela's gem is the Intrepid. It's a rebranded Vortex Viper comparable to about a $1200 scope you can sometimes find pretty cheap.