If you ask the question "What's the best degree for Data Science?" you'll get dozens of different answers. The sheer amount of different opinions might leave you wondering which degree is the "best", and there isn't a simple answer. One person's "best" degree is another person's "worst."
Trying to make sense of all those differing opinions? I've done the hard work for you. This is where statistics is actually very useful (and it's one of the popular choices for degrees, go figure). This simple bar graph is the result of a meta analysis of opinions from DS bloggers, academics and data scientists (see below for the reference list).
The clear winners: Either teach yourself, or get a masters in data science. A couple of surprises: astrophysics and philosophy made the list. In my mind, I'd hire an astrophysicist in a heartbeat. And philosophy? Well, there's certainty a great grounding in logic there, although ask a philosopher to define "data science" (or anything else, for that matter), and prepare yourself for a very long conversation...
A big caveat: getting a degree should be looked at as a stepping block, not a train ride to a destination. No single degree is likely to get you in the door. For example, if you're considering a non-DS degree, you'll probably want to supplement your lack of DS experience with an internship or boot camp. And if you have no degree, then you're going to want a lot of practical experience.
Methodology note: The bar graph is based off of the first few pages of Google search results. I only used popular data science bloggers, academic sites and well-known news sources. Sites with names like "101datasciencedegrees.com" didn't make the cut. A particular item was only included on the chart if it was mentioned at least twice. And, I stopped researching when there was a clear winner with 10 "votes" (this is sort of like a negative binomial experiment, if you're interested).