Best Linux out of the box for desxtop 750ti on haswell asrock MB

I don’t know if this is the right forum for this, but I was wondering what the best Linux for the above configuration might be. I want something that just works out of the box with a Mate, LXDE, Xfce windows manager preferably. Does anyone know if such a distro exists?

Doesn’t matter. They all ship the same Linux kernel and NVIDIA driver in their repos. There is no special magic sauce added to a particular distro to make it unique. Chose your distro based on the amount of software the repos provide, it’s release schedule, size of community etc.

I want the card to be installed by the installer with sound working. Answer the question provided please. Do you know of a distro like this?

The HDMI/DP sound driver isn’t even provided by nvidia (well, at least not through their driver package). It is responsible by snd_hda_intel which sits in upstream kernel.