Disclaimer: I actually love skills, and I love playing the skill monkey. However, in a cold antiseptic light, I am willing to believe that most of them lack the utility they ought to have. This is a great exercise; here's a different view...
A. Crucial. Everyone should have one of Athletics or Acrobatics: you never need both, but either one can be used to justify some sort of physical interaction, and it is useful for every member of the party. The one you don't take becomes "D", unless you are pursuing a concept.
If your DM is going to push you into social situations, then you also want one of Investigation, Persuasion, and Intimidation. Again, you never need more than one. Pick your preferred means of interacting with others in order to get information, and the rest become "D" (unless, again, "concept"). If you want, you can leave these for someone else in the party, but you risk being deprotagonized, so grab one of them.
B. Important only in certain campaigns. Of zero value (D), unless the DM decides to build a campaign around it, is Animal Handling if you're going to be riding things or have mounted combat. You don't want to be the only one not riding a hippogriff, or stuck with the covered wagon from your tool proficiency with land vehicles. Stealth. Unless you want to go off on your own, the party is only as quiet as the low dex dwarf. Completely useless if you want to live. Performance is only useful if you are a bard, or if you don't like the guy playing the bard and you want to show him up; otherwise D.
C. Someone should have it, but it doesn't need to be you. One person in the party needs to have each of Insight and Perception maxed to the gills: though more than one is not needed. It's part of why they're not good skills -- they present crucial information, but (a) it's often the case that the DM is going to give the info to whoever has the highest perception/insight anyways, and (b) one success causes success for the whole party. So does that make it important? Selfishly, I'd actually say no -- your character never needs it, because someone else will always have them. Unless you just want to be that guy. That guy is fun to play, of course, but it's a narrative choice, not a tactical one. In the same category is survival and arcana: as long as one character will build an ice fort for you every night, it doesn't need to be your responsibility; as long as someone can identify the weird magical thing, it's fine. It just never needs to be you. (At upper levels, religion eventually falls into this category too.) Finally, someone needs to know how to lie, and so one person in the party should have deception.
D. Rookie Mistakes. Seriously, you want Medicine in a world where tool proficiency with a healer's kit can make half price healing potions, and there are clerics, paladins, second winds, and short rests? Might as well take Nature: the guy with survival can tell you all you need to know. Maybe take if you're a druid and you want to act in character. Then there's History, only useful as an excuse to let the DM tell you what happened before your party began adventuring. You'd be better learning Sleight of Hand, so you can pick the pockets of people who don't have perception.
So, in summary:
A -- two skills everyone needs, one physical, one social
B -- one or two that you might need, but is campaign specific
C -- six skills that the party needs, but try not to be the chump saddled with them. Take one, two if you're lawful good.
D -- everything else.