Prioritize clearing story? (new player)

You should be good for awhile on events that require more than clearing fuyuki. I'd honestly advise either way as both have their positives. Playing through more of the story is more content and is fun as well as getting you a decent amount of quartz (Camelot especially is really fun). But for AP efficiency, you could wait for the next half ap story mode period to clear chunks of or all of the story as well.

As for Prisma, if you have Kuro at np 5, you don't necessarily need the crystallized lores yet and can skip on full clearing once you have all the mats you want from the shop

Prioritize Prisma for now. most of the events only require clearing Fuyuki so you don't have to worry about that. git all of Kuro's ascension mats and copies to np5 then you can decide if you wanna go for the story quest or farm more mats from the event. Personally, I'd stick with farming more mats.

Someone outlined this in another post. Be wary of levelling too fast by doing events. If you get to a high enough level eventually story mode quests won't refill your AP bar fast enough and you will have to progress through the story a lot slower

I’d argue to work on the Prisma event first. There’s always at least 1 week of downtime between events. This is the ideal time to A. Catch up on the story. B. Work on servants and C. Farming from dailies

Limited time stuff typically takes priority IMO

If you plan to be F2P, then never pass up a welfare servant, they are always worth it. Summon rate ups are a lie. I don't know how many of my limited SQs and tickets I spent trying to get the rate up caster or assassin only to get 3*s or another rider or saber... Shiki and Iri as welfares were godsends.