With Xubuntu 16.04, the experience is pretty good.
You can expect everything to work, except the fingerprint scanner. By everything, I include Optimus, which is the most frustrating aspect. However, luckily with this class of hardware, there is a bios setting to activate discrete video, in which case you end up simply with a Nvidia laptop.
If you need the incredibly good battery life of intel-only mode, you will need Optimus working. Note that if you are prepared to live with the non-LTS releases, there are very big advances in Optimus support available in Ubuntu 17.04 and it seems to work well with Gnome and Unity, unlike 16.04 where I recommend xfce (it has an older compositor which handles Optimus better when using the xserver we are stuck with until 16.04.3). People who try to get Gnome, KDE or Unity working on anything with xserver < 1.19 will have grief if they want two external monitors and Optimus.
I have SecureBoot off.
I document my ongoing experience here: http://timrichardson.net/index.php/technology/linux-on-thinkpad-p50