When you first start out, the only thing that really matters between weapons is level. Higher level weapons are flat-out better than lower leveled ones in every way. So when you unlock a new level of weapon, put your favorite skills onto the new one (you always get a 0 star version of the weapon with the minimum number of skill slots when you unlock a new weapon level, and it doesn't have any skills on it so you don't have to worry about skill removal which is hideously overpriced even late game.) As for the skills you should put on it:
-EXP+: You're beginning the game, nobody should be maxed out. EXP+ helps so much and should be on everything you use until that character reaches max level.
-Materials+: Badges make a huge difference, but you need materials to make them (you also need materials to make potions but those aren't as important. They never are important tbh). 1 thing to note is that
Materials+ cancels out with the effects of Stars+ and Slots+. So if you have Materials+ and Slots+ on a weapon, you don't get the benefit of either skill. (You don't need Stars+ and Slots+ to cancel out Materials+. Stars+ and Slots+ do however work with each other but are more useful later for when you actually need better weapons.)
-Rupees+: You need money. It doesn't matter what point of the game you are at, you need money. I honestly have Rupees+ on all of my weapons even over 500 hours into the game, it's THAT important.
Nothing else beyond that really matters early on, but Strength skills for your favorite moves should be priority after the above 3 skills. You mentioned the Element+ skills which are... okay. Darkness+ and maybe Light+ and Water+ are the only ones you should use. Fire+ is pretty useless and Lightning+ actually ruins combos on most weapons so that should be avoided.
There's also locked skills which are more of a hassle early on. I'll give a quick summary of what can be behind each lock:
-1,000 KOs: Can increase item efficiency and other small effects such as filling the special gauge quicker. You should ignore these because these skills are completely worthless.
-2,000 KOs: Increases damage against certain enemies. Most are way too situational, but the 2 best ones are VS Dragon and VS Undead as they both cover a large range of enemies that are also some of the most annoying enemies. (Lizalfos, Dinofos, both Aeroflos, Volga, King Dodongo, and Argorok for VS Dragon, both Poes, both Gibdos, Darknuts, Stalmasters, and Wizzro for VS Undead.)
-3,000 KOs: These are a huge pain early on and should be avoided like plague. They offer neat bonuses (most of them increase damage by a significant amount) but also give a hindrance that usually hurts more than help early on. Want to do more damage? Well you can only heal 1/4 of a heart at a time (even when you drink a potion or level up!) or you lose your ability to shield. Want to not be able to be launched? How about being able to automatically recover health? Well you're going to take double damage for that.
-4,000 KOs: THESE you should get. Their bonuses are better than the 3,000 KO skills AND don't have any negative side effects! The best one agreed on by all is Hasty Attacks. This skill lets you attack faster. Basically it should be used on almost every weapon with a few exceptions (Young Link because he's in Focus Spirit a lot and HA doesn't increase your speed in Focus Spirit, and I'd also vouch for the Horse because it already attacks fast and HA may make it uncontrollably fast.)
-25,000 KOs: This can only be 1 skill. And no matter what point of the game you're at, you should let out a sigh every time you see this. Not only does it take way too long to unlock (and remember, you can't remove locked skills until you've unlocked them), but the bonus barely does anything. It brings up that weapon strength (assuming with 0 stars), to 300. This is nice on lower leveled weapons, but on level 3 weapons, they have a base damage of 280, so only 20 extra points of damage is hardly worth it. On a 5 star level 3 weapon, it gives it... 30 extra points of damage (420 --> 450). You also need to unlock the 25,000 KO skill on the Master Sword first before you can unlock this skill on other weapons (but the M. Sword has its own special version of the skill that is actually helpful, 200 extra points of damage!) so it'll be a LONG while before you can even use this, and it's honestly terrible.
Another thing to note is that you can only have 1 locked skill from every tier (besides the 4,000 KO tier, you can have 2 of those skills which is good since those are the best ones!). So late game weapons usually have 1 2,000 skill (VS Dragon), 1 3,000 skill (No Healing), and 2 4,000 skills (Hasty Attacks and Finishing Blow+, but Special Attack+ is better on some weapons). The 1,000 KO and 25,000 KO skills should just be ignored. :/
So an early game weapon should look like this (using Lana's Book as an example):
-EXP+
-Materials+
-Rupees+
-Strong Attack+
-Strength IV
-Whatever else you want
And a late game version of that weapon should look like...
-Hasty Attacks
-Finishing Blow+
-No Healing
-VS Dragon
-Strong Attack+
-Strength II
-Strength III
-Strength IV
Also I know this is advertising and TBT doesn't like this but it's related to the topic so I'll post it anyways (I asked Justin a few days ago but hasn't responded. If he says no, I'll edit this part out.) I've been making guides for this game for a few months now so you can see specific skill sets for weapons
here.