If you go for x360 or PS3 be aware that this party games were much worse on PS3 until the middle of the generation. I still think this would be a sweet spot for the generation & the X360 would have some backwards compatibility with original Xbox games. PS3 started the trend of modern playstation exclusives that're must plays with Uncharted 2 & Infamous though.

Regardless there's a ton of great games from that generation & not all are backwards compatable on modern Xnox (if you go that way), but I do think you could get some great value out of the Xbox Series S as you can buy old games online & could subscribe to gamepass for modern indie games or smaller games if you want to check them out.

I know you mentioned you aren't into modern titles, but it could just be the specific genres you are looking into as there are a ton of different types of games now.