Skills' priority worth to be lvl 10

I look at it more as a 'love' thing. The vast majority of servants do their job just fine at level 6 skills, with the exception being support servants like Waver, Merlin, and Helena.

Ideally, you're choosing skills that have the most beneficial scaling and benefit the most from having the shorter cooldowns. So the servants you probably want to choose are the ones who are best for taking on challenging content. Euryale, David, Mash, Cú, Jeanne, these are all servants who need that low cooldown to make sure their skills are ready and available on the turns you need them to be so you can survive that extra turn or deny the enemy their NP. Cooldown management is super important for hard content.

Funny enough I asked the same question on Reddit couple of days ago. To summarize the responses from othwr players: there are a few criteria in play

1. Maiority players 10/10/10 their favourite servants first. This is because favourites are used all the time regardless of gameplay. I personally did this too, and then try to build a team around my favourites.
2. Servants who are too good gameplay-wise to ignore (e.g. Waver, Merlin, Tamamo if you are lucky enough to have them, Hans, Mash etc) are also maxed. Depending on preference favourites vs the need for better gameplay, ppl prioritize accordingly.
3. Niche servants who have a use for lower cooldown, or have saved players in certain situations are maxed selectively, maybe not 10/10/10 but somewhere 4-6 skill level.

And as usual, materials and QP will always be hell. So you decide the order of leveling (if at all) depends on who you need at the time, and how many resources available.
Hope that helps.

Edit: some people always max battery skills first for faster farming :)

To me, L10 is generally more about cooldowns than the better effect, though sometimes that's important too (e.g., an NP charge of 20% or 40% at L10 makes a self-charge + Kaleidoscope/Imaginary Element work).

For cooldowns, I typically look towards those that start at 7 (thus, CD is 5 at L10), particularly steroids that have 3 turn duration. This gives them a nice 60% uptime. A few skills, like Robin's poison, last 5 turns, and that skill also can have a 5 turn CD, so that gives it a 100% uptime. But this isn't the only concern--I don't ignore the higher CD skills, nor will I raise a skill to 10 just for the 5 turn CD--it depends on whether you'd really want to cast that skill as often as possible in longer fights.

For me, I don't buy into waifu/husbando meme, so all decisions (including grailing) are100% for gameplay.

Chloe battery is actually the best battery, it makes her arts cards puke stars.

Dedicated supports are the lv10 must. Casgil, Helena, Waver...specially Hans and Waver.

After that, priorize 3-turn skills, specially if they have low cooldowns, or if their buff is AOE, like Leônidas buster buff or Mash def-up.

Someone said that a 10/10/10 servant is for love/utility because is so expensive (QP and materials)
Which skills you should enhance to lvl 10? I think offside of love and super support servants (wever, Tamy, Merilin, etc.) choose those skills that you will use more don't mather if you use it because is useful or because you like it, enhance till 10 a skill that you will not use a lot will be a waste of resourses most if is on a servant that you don't like.

I think your favorite servants should get first priority. Personally, I try to max battery skills first because farming is life. Second priority is buff skills with priority going to farmers' mana burst/charisma/tactics/etc. and party wide buffs. Lastly, skill cooldown and survivability for challenge quests.

tldr:
1: Waifu/Husbando
2: Battery for farming
3: Buffs for farming
4: Cooldowns/Survivability for Challenge Quests

Always factor in how often you use a servant in your choice. If leveling skill A has a "worth" of 500 and leveling skill B has a "worth" of 200, skill A seems like the clear choice.

However if you use the servant with skill B 5x more than the servant with skill A then the value switches and skill B is probably better to level.

Cool down matters for servants that will be involved in super long battles, like today's 7-wave Dantes challenge quest. For most 3-5 turn farming, CD just isn't important.

So, skills where every percent matters, like NP battery, go to the max. Frontline goes to max before backline since CD can matter to them in a slightly longer battle.