Why not go for something like the Xbox Series S? It is in your budget, is a powerful little console, gets you the bells and whistles of next gen, and - if purchased through the Microsoft store since it’s all digital - can play older games.

The only bummer about the XSS is the fact that it’s all digital, so if getting old used games is important to you, perhaps you look at an Xbox One or a 360! :)

Happy gaming!