So Dungeons and Dragons 5th Edition. Skills (and their mostly-sad cousins, tools).
There are two important skills, and they're really important. Stealth and Perception. There are a handful of situational but useful skills. Acrobatics and Athletics (which are mostly just one skill for different classes), sleight of hand, investigation. And the social skills, which vary widely based on table. The others suck.
So why do we care?
Because these are all the mechanics (practically) for everything that happens out of combat! Which is most of the game! Maybe not at all tables, but most games spend more time and thinking out of combat than in combat.
So what's wrong with skills? Let's look at the worst one. Medicine, and it's associated tool the Healer's Kit. What does the healer's kit do? It lets you stabilize one dying person without a skill roll. What about medicine? Same thing, but with a roll. Bleh. No one does this.
Why is this bad? Because it's too narrow. Go look up Medicine, the scientific (and practical, shh don't tell any doctors!) pursuit. It covers a lot more that that stuff! Actually seems like a lot of stuff adventurers, who travel to strange lands and through dangerous places, encountering and causing harm, might find useful.
What's the solution? Read this really broadly. Anything that involves the health or failure thereof of living creatures or dead creatures with anatomy (like zombies).
Anything involving the loss of health or injury of a biological creature. Diagnosis, what caused an injury. Do players notice if the creature they're attacking is resistant to their attacks? That sure sounds like Medicine to me! What about what kind of weapon caused an injury? Yep, also sounds like Medicine! (wait, what about investigation? read on) If you're travelling through a desert or a poisonous swamp, trust your local Medical person to help you avoid the worst effects (usually advantage)
Did the silver weapons cause worse wounds? Did the wounds heal faster than normal? Is this thing... not... quite... human?!? All questions Medicine can answer. Did this ancient society die of outside attacks or a plague? Yep, Medicine! (and history, and investigation? maybe!)
So there you go. I won't go through all the skills, you get the idea. Consider skill proficiency *at least* a bachelor's degree in a related field. More if a player can give a good explanation.
What about tools?
So what about tools? What about overlapping tools/skills?
Tools, by RAW: If something is covered by both a tool and a skill, advantage on the skill. So fine, do that for skills too: if two skills overlap, and you have both, roll the higher with advantage.
But wait! What if I have two skills and a tool? No, you don't get double advantage. Why not? Because games don't model very low/high risk well and it doesn't lead to more interesting choices. You can get advantage but more changes scope.
Let's suppose people are mysteriously dying and your elven adventuress, Herlock Sholmes, investigates. She has Investigation, Medicine, and a Healer's Kit. Since she has two skills on point, she chooses the higher of Investigation and Medicine and rolls with advantage. But since she has a third level, she gets two things: She can't be wrong. Even a failure results in her finding what someone else would find on a success. Second, she sees deeper.
"These wounds were caused by some kind of animal," vs. "These wounds were caused by an animal's claws, but with a deliberate intent and a good degree of intelligence, meant to cause silent or rapid death, by a creature of above human size and strength." Another level (Investigator's Kit maybe?) "The attacker was using their own claws but has studied anatomy in a formal sense." Another level? "At Westchapel college" another? "From Dr. Sorkin." Another level? "graduating within the last two years"
That's it! Let players use the skills in all sorts of ways! Tools too! Even more if it's fun!