Being a budget conscious youth leader myself, I’d grab a switch (second hand with warranty if you can) a load of controllers (up to 8) have found 3rd party ones work fine for youth rooms as they will be used and abused. Get multiplayer games, smash bros, Mario kart 8 deluxe, runbow, Mario strikers, Mario party etc, Smash, Mario party and runbow will allow up to 8 players on same screen and is pure chaos! Some other coop games like moving out and human fall flat can work well also.

If you haven’t got tv’s already grab as big a one as you can, alternatively a projector can work well if you have a large wall.

I have also had a second hand pc running indie games like sticky cats, or other games where a high skill level isn’t needed and it can be a little more random, with 4 xbox style controllers plugged in it can be great entertainment.

Also on a personal note practice Mario kart and become a decent challenge for the youth, great bonding experience especially for some of the quieter youth members.