My most-shot firearm is my Smith & Wesson 15-22 (second place being my S&W Victory 22lr pistol I shoot in conjunction with it), set up to be a fairly faithful copy of my primary 5.56 AR.
To fill your criteria, I would recommend a S&W 15-22 sport (the mlok one), upgraded with the TandemKross extractor and firing pin kit here:
https://www.tandemkross.com/essential_maintenance_kit-sw-mp-15_22
In my experience, the 15-22 doesn't have 100% reliability firing or extracting with the OEM extractor and firing pin (It's like 98% there but when you're firing as much as I do through this gun, that's a noticeable rate), but the TK pieces are machined a bit more precisely and make the gun run like a Swiss watch. As long as you clean the gun regularly (I run the gun until it gets so filthy it won't cycle reliably anymore, that's when I know it's time to clean it), with that setup it should be awesomely reliable and makes for great, cheap practice. Also make sure you keep an eye on the ejector - just keep it snug and angled where its position doesn't impede the cycling of the bolt. I find my 15-22 absolutely loves Federal Auto Match, Federal blue box bulk, Aguila copper plated, and CCI Mini-Mags - that is absolutely why I specify those are the brands of 22lr I'll accept in BST trades. It will cycle lower velocity stuff, but might be a bit sluggish by comparison, especially as it starts to get dirty.
That with your choice of red dot, and either a LaRue MBT-2S or Geissele trigger, and you'll have a lightweight, fun, cheap, and reliable little carbine to train, hunt, plink and compete with to your heart's content. I 100% recommend it, as my 15-22 is one of those guns I *always* take to the range.