Hmm...
- Grind the Ember Gathering quests for EXP cards. It's why I always try to roll for Tamamo Cat in the beginning - AoE NPs make farming and mobbing so much easier. I wouldn't waste AP on the Treasure Vaults at the moment (except for the Weekly Missions) - once the events roll in usually they give loads of QP.
- Level up whoever you're using. Levelling up servants increases their base HP and ATK. Try to have at least one servant of each class levelled to cover all bases, two of each with differing NPs is ideal (usually 1 for single target NP, 1 for AoE NP, 1 for support, etc.).
- HP/ATK Up is useful for adding a bit of meat to health or attack power, but the 3* ones cannot be rolled or dropped - only in the shop or as event rewards. You need 20 of each 3* HP/ATK Up card to max out a character (for the moment...).
- Ascending is more or less mandatory to hit level requirements. Save your mats for them, especially the rarer ones.
- When you can, level up the skills of the servants you use. Servants usually gain more skills after they ascend, and there are break points in the levelling that will reduce the cooldown of the skills by 1 turn (at Level 6 and 10). Some servants are basically usable (read: essential) because of their skillset. Levelling them up is a bugger though - skill mats are used for ascending too so you'll always be looking for the likes of Phoenix Plumes, Pages, Lanterns, etc. Events are a great way of replenishing these, grinding the Training Ground missions for mats isn't too bad, and later chapters will have levels that are better for farming specific mats. Crystallised Lore is required to max them out, and they usually only appear as end-of-chapter or event rewards, so use them wisely.
- Always look to level up your servants' NPs with duplicates. Duplicates are rarer for 4*+ but will usually improve their damage and effects massively.
- Make sure to do your Interludes and Strengthening quests. These give out gems and most improve skills/NPs of specific servants in your possession. Interludes will have certain requirements, like base Lv and/or Bonding Lv.
- Bonding Lvs matter more than most think. Bonding Lv 5 onwards produces quartz (or apples if low level servant), and Bonding Lv 10 gives you a servant-specific CE which boosts them and/or the whole party. You'll be grinding for those Bonding Points sooner or later (some shop CEs will help later on, so start saving those Mana Prisms!).
- Once you're happy with your servants' levels, you can grind the same Ember Gathering quests to burn the EXP cards. Gold and Silver EXP cards both burn for 1 Mana Prism, and doing the 30AP Daily Quest should reap you 8-9 Mana Prisms a run.
- 3* cards in general (servant/CEs/EXP cards) are OK for burning for mana prisms if you're not going to use them. I usually have at least 1 of each 3* Servant/CE and "limit break" them with 4 other duplicates before burning extras for mana prisms. Same with my 1*/2* CEs/servants, though burning them only gives pitiful QP and no mana prisms, and are usually not even worth using for EXP. As a side note, more or less all of the servants I have that are 3* and lower have maxed out NPs.
- 10-roll the FP when you can, especially now as we're all (re)starting and the card pool is much smaller. As I mentioned earlier, FP rolls give out the occasional 3* servant or CE, which can be burned if not required (see above) for more mana prisms. Plus, 3* servants are definitely usable and some 3* CEs are just budget versions of the "standard" 4*/5* CEs (Ley Lines is useful for starting a servant with some NP gauge charged, sorta like a budget Kaleidoscope).
- Try not to accidentally burn gold CEs and servants unless you really don't need them. There are more safeguards nowadays but it can still happen. Burning gold servants actually give up a Rare Prism, another currency to use on rare items in the shop.