Hasty Attacks is a must for everybody, except Young Link; use Focus Spirit+ instead. Young Link's entire gimmick to is stay in focus spirit as long as possible, and because Hasty Attacks has no use when under the influence of magic, you're far better off using the skill that increases the damage done in focus spirit. They are both 4000 KO skills.

Special Attack+ increases the damage done to the attack that drains the yellow meter in the top-left corner of the screen; it is activate by pressing either the X or A button, depending on your controls. You should also use Finishing Blow+ instead (which increases damage of the weak point smash), unless they have a good special attack (eg. Zelda, Sheik), in which case you can choose whichever of those two you prefer. They are both 4000 KO skills, and in addition Hasty Attacks (or Focus Spirit+ for Young Link), it means you can't add any more 4000 KO skills.

You can add either No Healing or Defenseless for an easy damage buff. They are both 3000 KO skills and have the same increase in damage as each other, so choose depending on whether you would rather be able to block enemy attacks or heal properly.

If your 5-star 8-slot weapon has the locked Legnedary skill, you're going to have to unlock it even if you want to remove it. I personally like to have Legendary on my weapons, but it's not mandatory. It depends on how many other skills your character has to work with and whether you feel like grinding 25,000 KOs will one weapon.

Element skills are sometimes worth it, but it highly depends on the character; you should look into specific character to see if they recommend them.

Other than those, just add the Strength skills to the attacks you use most, or EXP+ if your character is a low level.