Try centerfire cartridges...
243 Win. 36c per bullet. $1.20 per brass shell. 0.35 to 0.50C per primer. 24c worth of powder, IF you can find it.
6.5x284 50c per bullet, $1.20 per shell, 0.35 to 0.50c per primer and 27c worth of H100V powder.
If you try to buy that kind of ammo factory loaded you are typically looking at $2.80/shell and it would likely not be optimized for your rifle anyhow. This is high ballistic coefficient ammo loaded with the heaviest Berger bullets for the caliber.
Of course, generic 223 and 308 ammo is cheaper especially now that the ammo supply seems to be settling down.
For plinking, there has always been the 22 hornet. Provided one has brass, it can be loaded from mild to quite impressive velocity, takes just a tiny bit of powder. I just have the problem that our hunting regs forbid any kind of centerfire for night hunting, including the hornet.
So I am stuck with severe ammo shortages, less reliable ignition, inability to reload, poor ammo variety. All by LAW... I have also noted that it seems to be getting harder to get a quality rimfire rifle, especially in the 22mag. So far I have had a CZ and the most expensive stainless model Savage makes and they have both been worthless. Neither substantially better than 5-6moa at 100 yards. Given that every centerfire rifle I own will shoot 1/2moa or better, it is either the rifles or the ammo or both. Since reloading is out and supply is virtually non existent, I don't know what to think.
The Savage specifically is lacking quality in every part and concept, like buying a Fiat. NONE of the 4 magazines I got with the rifle worked. All had to be "adjusted" to fit the magazine well and the magazine guide bar better to the point that one could actually cycle ammo through it. The "bedding" concept is a complete joke. There is basically a bushing screwed into the front and back of the receiver and the bottom of those bushings is the only contact made between action and stock. The stock is so whittled away to allow the bushings, trigger mechanism, and magazine guide some room that is is about paper thin. Now I have entirely converted to Savage for my centerfire rifles since I can do all of the gunsmithing myself on barrel changes, but the rimfire rifles look like they were conceptualized in a basement in China.
Anyhow, I am sure I have waxed enough about my rimfire frustrations. Our overcomplicated hunting regs force you to go out and get a different weapon for what seems like every game species and season. Coyote hunting during the day - 243win. Coyote hunting at night - 22 mag. Early deer season - used to be shotgun, but now I can use a "pistol caliber rifle" in 44 mag. Late deer season - Muzzle loader. Turkey - smooth bore shotgun. Migratory game birds - shotgun which can only hold 3 rounds and using steel shot. etc etc etc. A turkey tag costs $20 for 1 bird. Seems hard to justify doing it.