Sorry if I forget something, but here is what comes to my mind atm...

Save up for rebates or other purpose:
- Seal scrolls
- Summon scrolls
- Charm material
- Refinement runes
- Mysterious cave keys
- Battle Armor threads
- Coupons (use when you can do a full Fukurokumaru deal event)
- Skill Breakthrough material (wait for some ninja you really want to get fully BT, dont waste it)

Do not save up (no rebates / no need to save up):
- Moon / Sun scrolls + mysterious stones
- Training potions
- Secret scroll pages and elixirs
- Mount Myoboku material
- Purification material
- Ninja assist link material (Chimes and bond scrolls)
- Battle Armor cloths
- Eight gates training points
- Treasured tools material and scrolls
- Magatamas
- Runes
- Mood scrolls
- Awakening material
- Equipment upgrade material
- Purification breakthrough pills
- Those Nature chakra training scrolls (not sure what they are really called...)

That´s all I can think of right now... maybe someone will add something whats missing xD

you can stave stamina potions to attempt at some point to get into ino flower with them, but you should be sure that you get to the place you want, if you know usually there are few people every event there i won't recommend

Hmm.

In addition to what BattleCrier said above, you may save up your Sun and Moon Scrolls also during the 3rd to 4th week of the month. It is for the Season Mission which will ask you to spend a specific amount of Moon or Sun Scrolls to accompli*.