What other calibers have you shot? I’m just thinking everyone here got in a super pragmatic thought process but maybe another thing you might want to consider is the actual shooting experience itself. Personally I find most .20 cal rifles super boring, and I don’t mean to that insult anybody with one, but cheap ammunition or not I would have been seriously misled had I asked and taken the same advice as given here, and even I was about to say .223 until I wrote out my initial response.
I’ve fired a fair few .223 rifles, Savage Scout 110 (just a short savage 110 action) a Savage Axis, Howa Mini, and as nice as most of them were as rifles (the axis felt clunky) I found .223 was underwhelming, if not boring to shoot. Thats not to say anything less of people who enjoy .223 because there’s endless literature to back its merit and I’m not opening that can of worms. I rarely ever shoot past 150yards just because of my location and finding the time, and I still choose to own and shoot overkill, impractical and expensive hunting calibers (308, 450bm, 300wm) simply because I find it intoxicating and sending spicey hot rounds down range puts a smile on my face. .308/7.62 is certainly more expensive but to play the devils advocate here, you might find it more fun?
On the topic of the gun, Savage/Ruger/Tikka and Howa all make great price point rifles, some even with scopes for all the calibers in this thread mentioned, the action is important but the glass is key, you can live with a budget friendly finish on a rifle but you’ll have a bad time looking through crappy glass.