Traditionally, IBM and Lenovo has had good support for Linux.
I can't speak specifically for the X200, but I can for the individual parts in it. In terms of speed, my Sony has a P8500 and runs Linux just fine (good processor actually). Where you may have issues is with the wireless card, it's probably going to need the Iwlwifi driver, which frankly, I think isn't all that great, it works, but shutting down can be slow, it's better than it used to be though. Other than that, you should have no problems. Worst case, buy a different wireless card for $10. If you have an old SSD, throw that in, newer ones will not be any faster due to the Sata2 speed. With that, the system will perform similar to a modern mid-level notebook, or at least feel like it.
I initially wrote a post about encouraging you to reconsider the x201 for future proofing reasons but after researching it, there's almost no difference between the two. Both have an 8gig limit, ddr3, sata2, same screen resolution, Win10 support... Even battery life and processing power is similar. The only real benefit over the x200 is that the x201 adds a touchpad, 300meg wifi (vs 150), and more readily accepts 8gigs of memory (the x200 requires specific memory and/or bios tweaks to do so).
