no it would not be the wrong time to get a 360, there are literally hundreds of great games for it, and the next one might not even run a disc drive, so you cannot get all the games for the 360 on the nextbox.
personally, I have a ps1, ps2, ps3, xbox 360, nes, snes, n64, gamecube, wii, wiiU, gameboy, gameboy advance, DS lite, 3DS, commodore 64, ancient atari.
and will be getting all the next gen consoles as well, but I am collecting them to have everyone of them so I am able to play them off one tv in my man cave when I move.
so, yes it is worth it, even just for the back catalogue