Welcome, Mark.
If the link I added is not correct, let me know.
Have you considered the maintenance aspect of that tile on a kitchen splash? 'Specially behind the stove?
I would want to rough up the paint with a very course sandpaper before trying to tile the wall. There is no best thinset mortar for your application, but there are many good ones. All you need is a good quality thinset mortar meeting the requirements of ANSI A118.4 when mixed with water. It'll say that on the bag.
I would use a white mortar.
My opinion; worth price charged.