Inventory of materials.

Long answer short: Apart from class pieces and monuments, you can never have too many of something. For example, I had over 100 knight medals. MHXA then takes 110 of them. You could be rolling in chains, summon Ozy, and realize 150 isn't quite enough for him.

And it isn't just 5* servants: Billy the Kid takes 110 bones and nearly that much dust. So during events, buy out the shop. It doesn't matter if you already have a bunch of something. You're guaranteed to need it.

And as far as saving them goes, I'd only do that if you have a specific servant in mind. If you have no intentions on summoning on banners with a Saber on rate up, then why hoard those gems? Use them on the people you already have and use. If there is someone you want and plan to summon, level, and 10/10/10 immediately, save enough to do that and do whatever you want with the rest.

(Except maybe pieces and monuments. Even if you whale and want to ascend everybody you'll probably be okay there.)

The more you have the better. Just get everything from every event shop and you'll be somewhat safe.

As much as possible of as many things as possible, especially when you are working on skills which gobble things up so quick.

Babylonia gave you over 100 void dusts... Doesn't last long when you have ~5 servants with skills that take 30-60 a piece to level.

Don't kill yourself farming unless you have a particular ascension/skill you want raised, but never leave material in event shops. If you don't need it now, you will in the future.

your question is basically 95% of fgo. no matter what you do, you'll need to farm anyway. you can never have enough materials.

especially fangs. it's like every servant i want or have require fangs. that and metals and dust and pages. i'm in a desperate need for the hunting quests.

Personally, I set up a spreadsheet with all the servants I want to level up (ascensions and skills), along with what mats I need. I also can set up my priorities so when I go to spend a mat, I can see who else needs them and how much, so I can decide who should get them first.

I first started with the servant planner on this site, but all it can tell you is what total mats you need, and I could't get a sense of being able to prioritize my spending, so if those who work on the tool are reading this, that would be a great addition.