Is there a specific undergraduate degree pre med student should acquire in order to stand out to medical schools?

As long as you complete the required courses to be considered for medical school, you can major in anything. Most students will major in biology, chemistry, or something similar so they can start getting an understanding of the field and start taking upper level biology courses but I have also seen students major in history, English, etc. so they are more well rounded or have other interests.
Typically medical schools require a year of chemistry, biology, and English plus courses in physics, organic chemistry, math, and biochemistry.
In order to be the best applicant you can be, you will want to volunteer in the field - whether it is a hospital, private practice, clinic, etc. This will allow you to understand a day-in-the-life of the professionals, determine what kind of medicine you are most interested in, and speak with the doctors about their own academic and professional journeys. This will also give you more to talk about should you be asked to interview in support of your candidacy.