The 22 LR has been around a very, very long time for a reason.
It has probably put more food on the table than any other round.
You can still afford to shoot it enough to become proficient with any firearm on an instinctive level. At a minimum, it will cost you over twice as much to do this with any other round.
Right now, I own centerfire rifles in 223, 22-250, 243, 6 mm Remington, 6.5x55, 6.5 Creedmoor, 270, 7mm-08, 30-30, 308, 30-06,300 Weatherby Magnum, 7.62x39, 7.62x54, 303 British, 35 Whelan, 375 H&H, and 460 S&W.
I have two 22 WMR's and nine 22 LR. (Note, I have been collecting for over 40 years...)
I shoot the 22 LRs more than the rest of the lot combined.
I practice for big game shooting by shooting practical targets with the 22 LRs (this is fancy way that I plink at longer range targets). I also play "Kick the Can" with my brothers in a range that we have set up on the ranch where it is safe to do so. I have permanently disposed of more pests and varmints on the ranch with a 22.
It is far too easy to be seduced by performance on paper. The performance of most of the cartridges on my list is indistinguishable on the shots that matter. Bullet placement and performance are far more important than MV and ME in any but extreme circumstances. However, I have not been recently attacked by a Cape Buffalo (or a range bull with a really bad attitude) out on the ranch lately. Explosive bullet performance is colorful and impressive on varmints, but dead is, after all, dead. And it does tend to gross out my pre-teen great nieces, daughters, wife, etc. And I prefer my hamburger ground, not blood shot.
A 22 LR will make you a better hunter since you will have to learn how to stalk, be quite, and wait for the right shot.
There is much wisdom behind the selection of a 22 LR over the other cartridges. Use it to become highly proficient and safe while you take your time to think about what the next toy will be.