I’m looking to spend $500 or less for everything
That narrows it down a little.
In this price range, you have to realize that the main compromise will the be the scope. IMO, the choice of rifles remains the same, but if your budget can stretch an extra $100, a VASTLY improved scope could be had.
The Savage Axis 2 XP comes in a package with a Bushnell scope. The Axis 2 now has the adjustable AccuTrigger which corrects the chief fault of the original Axis. IMO the addition of the AccuTrigger makes this rifle hard to beat in terms of value for money.
I own 2 Axis rifles in varmint calibers and I’ve shot hundreds of rounds through each without a hiccup. Accuracy is stellar with no qualifications.
SRP is $484 for the rifle/scope combo, often found for less online or if you watch sales.
Next up is the Ruger American. Ruger offers this rifle in a combo with a Vortex Crossfire scope.
In my experience, this is also an excellent rifle for the price. Adjustable trigger and excellent performance out of the box. The SRP is $639, but the combo can usually be found for (just) under $500 online and again watch the sales.
However… My test of the Vortex Crossfire was an epic fail. I got 2 defective ones right out of the box and I never shot around with either scope mounted. I ended up moving on never tested the final replacement. If you go this route, be careful and if the scope reticle cannot be focused to your eye using the usual procedure, return it!
Thompson Center now has the Compass as their rifle at the entry level price point. I have not personally tested this rifle, but I have handled them at trade shows and the fit, finish, and refinement is better than both the Ruger and the Savage, but it comes at a slightly higher price point for the rifle.
Rifle only is $399, I see them in the low $300 range all the time online. This could be an excellent option as it would leave you about $150 for a scope of your choosing.
There are other options, but this really covers the 3 that I think are the best performance per dollar spent. All of these rifles will shoot at MOA +/- a small percentage with good factory ammo. That kind of accuracy was hard to obtain 30 years ago at 3 to 5 times the cost, much less in the entry-level space.
Now which cartridge? Take your pick and don’t overthink it. You are not hunting African game, you aren’t going to be facing a charging grizzly in the willows, and there are probably 50 suitable cartridges that will all make a mule deer dead.
You can’t go wrong with the .270, 30-06, 308, 7-08, or if you want to jump on the 6.5 MM bandwagon, the 6.6 Creedmoor. All of these are good choices, all have excellent factory ammo options.
Finally, PRACTICE. Benchrest shooting is NOT practice. Real practice is from realistic field positions including prone, sitting, on shooting sticks, and standing.
Grouse