To the OP’s question, and well considered criteria:
Short version:
Find a Ruger American Ranch, Howa 1500 or CZ 527 in 6.5 Grendel or 6mm ARC and live happy. Tolerating more expense and recoil, almost any rifle in 6 or 6.5 creed, 243win, 7-08, would be a small step which adds a LOT of options to your list, however.
Personally, I’d be getting a Ruger American Ranch in 6 ARC when available, or 6.5 Grendel, with a very close second to a Savage 10/110 or Ruger American in 6.5 Creed - preferring an AICS mag compatible model, AND conceding I would probably swap it into a Boyd’s laminate wood stock, giving me options for a bottom metal change if so desired.
Long version:
Items 2, 3, and 5 are about the chosen cartridge. 6 arc, 6.5 Grendel, 6 and 6.5 creed, 243win, 7-08 are largely the only cartridges which I’d be considering in your shoes.
Items 1, 3 (somewhat), 4, 6, and 7 are about the chosen rifle. Lots and lots of options - the price is the criteria which culls the list the most, and will be the biggest limiter in your search. $500 gets you close, but it’s pretty hard today to satisfy.
Line by line:
7) Conceding immediately that removing #7 from consideration: 1) opens your options significantly -as in only about 5% of the market would have fit #7, whereas 95# of the market could be considered if you drop #7 as a requirement - and 2) shooting with irons at 300yrds is highly dependent upon your target - past generations thought shooting at 300yrds was very difficult largely because they were shooting irons (or poor scopes) and didn’t realize their self imposed limitations...
1) Remarkably easy to satisfy. Most models on the market for the last 20yrs are capable of delivering MOA or sub-MOA accuracy. Pretty hard to screw that one up. Ruger, Tikka, CZ, Savage, Winchester, Browning, Howa, Weatherby... pick your poison... personally, the only brands/rifles I would not buy would be Remington and any mil-surp rifle.
2) Other than rimfire ammo, almost all cartridges can be reloaded. SOME cartridges have more or less market support than others, or have nuances which frustrate reloaders, but virtually everything can be reloaded. 7.62x39mm is one which has some headaches; the .311” bullet is frustrating, with very limited market support. Many guys do shoot .308” bullets in x39’s, but there are prettier girls to dance with anyway, so I wouldn’t bother.
3) Hunting requires more momentum on impact than target shooting, but for 100yrds, even 300yrds, this really only knocks off the 22cal centerfires. 223rem will do the job, but it comes with some concessions which don’t apply to larger bore diameter cartridges. Hunting deer at 100yrds and less is an easy task, even 300yrds and less, so there’s not much sense in burning more powder, losing more lead/copper, or tolerating more recoil than needed. No 300win mags or 7 rem mags need apply here.
4) Many, many more models are available today than even 10-15yrs ago with detachable magazines. Some detachable magazines are better than others, especially in the context of casual plinking and hunting, opposed to high volume, high intensity shooting. I personally prefer rifles to be AICS magazine compatible, but I doubt that’s critical for your use.
5) To me, this is a non-criteria. The Non-compatible set is null. A 22LR can easily be shot out to 300yrds, so to use any centerfire rifle just makes life easier. 300yrds, when not shooting 22LR, is 223rem territory for me. But conceding to #3 above, a 6 ARC or 6.5 Grendel as a minimum standard for “no limitations” hunting is where I would look, and where I would buy.
6) Most major brands will offer a model in the $500 and under ballpark, if not, many more options are available in the used market. You might not get a detachable magazine with a sub-$500 base model these days, but if you can 1) buy used or 2) scrounge up another $200, you’ll find several options.
