What is a rule of thumb approach in which we choose between alternatives based on emotional or "gut" reactions to stimuli?

The correct answer is affect heuristic.

Affect heuristic refers to a mental shortcut people take when making decisions and solving dilemmas. Decisions and courses of actions chosen are influenced and driven by a person's emotions (comfort, discomfort, fear, surprise, etc.) at the time of making a decision. From the affect heuristic approach, decisions that feel and seem "good" are taken and decisions that feel "wrong" or "bad" are not taken.