Should I use a metal pan or non-stick pan for cooking salmon on the stove top?
This is a matter of personal preference.

Assuming you are sauteeing or pan frying (as it would make no difference for poaching, for example):

There is no reason that you cannot put butter and olive oil in a non-stick pan.

Use a traditional pan if you want fond (the brown flavorful bits) to form at the bottom of the pan, to use as a the basis of a pan sauce.   If your salmon is skin-on, that will help keep it intact.  You will want to oil your pan well.

Use a non-stick pan if your priority is making sure you keep the fish intact.