The Xbox Series X is this new top model, the Series S is their new more budget friendly model. The Xbox One X is the best last gen model and probably easy to find on FBM and CL for cheap. There is the plain Xbox One, which was the original last gen model until the One X upgrade. The 360 is ancient in comparison to all of those listed above and likely not worth the used price difference from an Xbox One. Also, I believe all Xbox games are backwards compatible, meaning the older games will work on the newer consoles (and work better).
PS - Again, the Series X is the brand new, hard to find model. The One X is the previous model that you can find used. Xbox loves their "X"'s.