What is the best MOS for a career in the civilian sector?

I would rank anything signal, logistics, or medical as the top MOS groups that convert well to the civilian world.
Almost any MOS can be converted to civilian employment. The obvious exceptions are things like infantry, artillery, ADA, etc. My son was a Satellite Systems Operator/Maintainer, and he was lucky enough to acquire all of the certifications he needed while in uniform to be able to turn that into an equivalent civilian career. I was a Psychological Operations NCO. That is most equivalent to marketing or advertising in the civilian sector. However, these jobs are extremely competitive, and civilian hiring managers can't draw the comparisons. The best opportunity for guys with my MOS is to work as a civilian contractor. but those companies require at least a baccalaureate degree. If I hadn't gotten a degree in business while I was in uniform, I'd probably be working in some low wage job. So, the bottom line is, you can turn your experience in any MOS into a civilian career, but make sure you do your research on the median qualifications that employers look for on the outside, and try and get those credentials while in uniform. If that means you have to pass up partying with your friends or watching Game of Thrones to attend night classes, then suck it up and do it. Even if you have to pay out of your own pocket (I didn't pay a dime for my degree under the TAP) it is totally worth the sacrifice later on. That doesn't really address the experience factor. If you serve at least two 4-year tours, then you can usually parlay that into civilian experience. If you only serve one tour and out then, even with the education /credentials, you may still be relegated to entry level jobs based on your experience level. Also, be flexible on location. Some of the best jobs may require you to move. Good luck.

Looking back, I think anything medical or IT (computer) related would make for an easier transition into the civilian sector.

I see a lot of former infantry working in law enforcement, construction, private security and outfitters. The tech side seams obvious, but you never know. I was communications for 11 years, and those jobs in civilian life didn't pay as well as being a plumber. After changing to artillery I ended up in architectural design and then in the rebar industry. I run a rebar company now as VP of operations and consultant. The most important tool that I took from the army was my leadership training. The second is multitasking. I run a rebar company, am a volunteer city emergency manager (FEMA Certified), run a Boy Scout group and have an MBA in Accounting. Good leaders are good followers, and any company recognizes that.