There isn't really a "Linux" for your phone in the same way that there is "Linux" for your desktop computer. Android really is "Linux" for your phone. And even if someone came out with a regular distribution for your phone, there would almost be no way that it would be as optimized to run on it better than Android.
As skittle said, find out if you can get Cyanogenmod running on it, it will probably be your best if you want something else. XDA forums is the go to place for phones. But in my experience, the original ROM that came with your phone will probably be the most trouble free. There are always quirks with custom ROM's, even on my Nexus 5 which probably has one of the largest developer bases.
And instead of mentioning your...