Xbox Series s or x ?

I'm in a similar boat. I have a couple of old 360s and they're RIP now. If anyone has an old 360 that works and not being used, I'd be happy to pay shipping. Otherwise, I may just jump to the Series X as well. I'm just hesitant to spend $600-$700 for a console right now. I have 50+ games I'd like to be able to still use, and the X would allow for that. The lack of backwards compatibility is why I never bought the Xbox One.

Yeah, I'm cheap. I'm curious though. If I play the 360 BF3 and 4 on the X, it will connect to the 360 servers, right?

Edit: I already have Xbox Live. I assume I can simply use my current subscription to play BF online, correct?
If you end up buying a Series X I’ll trade you straight up an elite controller for your stock one. If you are interested