What skills to max first on 5star servants

I would do Gilgamesh followed by Scathach and Ozymandias.
However, it all depends on your play style and whoever you use/is more useful to you.

Honestly if I were you I would straight up go for the best 5 stars to max out in terms of strength and how the skill would help out a lot in battle. By that I mean skills that either gives NP or makes attack stronger.

I would recommend maxing out the skills for Ozymandias, Gilgamesh and Scathach first since they are very good Servants and maxing out those skills will make it easier for you to use them to their true potential and will help you tons in hard boss battles. And give FPs everyday probably. Give those strong hard hitters the most priority but you could always go with favourites.

i would go for ozy and then gil, simply becouse ozy can be a pseudo support when you dont need him as a mail damage dealer.
and becouse i have cleo, so i love some ozy whit is third skill maxed

Gilgamesh is the most useful for farming and that's what you do the most on this game sadly, so him. 3>1>2 is a good order

For example, the last node of christmas features three servants on the last wave. That's Gilgamesh specialty right there, event nodes like that one are really common.

The rest doesn't really matter, pick favorites. Ozy can be used as a pseudo-helena, but that's it about farming usefulness.