[RPG] Which spell casting level do you use when casting spells with a Staff of Power

You can apply class abilities to spell casting from magical items

While casting from an item is not the same as a Casting a Spell action, it is still casting a spell. Unless a term is given a special definition in 5e game terms, you use the common definition for that term. You are casting the spell, the ability to do so comes from the item. For instance, the Staff of Fireballs:

.. you can use an action to ... cast one of the following Spells ...

Is no different, in this regard, to Wand of Fireballs from:

you can use an action to ... cast the Fireball spell ...

Jeremy Crawford has posted a number of answers we can point to in the time since this question appeared that verifies this really is the case. Each time he's been asked about a specific class ability the answer has been an affirmative. These were made when his tweets were official rulings, but since have been "downgraded" by the Sage Advice Compendium to his personal advice and perspective. While this is true, it still is clarification of the intent of the designers.

Metamagic

Can Metamagic be used on magic item casting a spell? Yes.

If a magic item's description says you cast a spell from it, you can use Metamagic on the spell. #DnD

and

Metamagic works w/ any spells that sorcerers cast. Wild Magic Surge can work w/ any sorcerer spell they cast. #DnD

Wild Magic

Can using a magic item cause a Wild Magic Surge? Yes

Yes.

Arcane Ward

Can casting from a wand/staff recharge Arcane Ward? Yes

Arcane Ward/Twinned Spell works when you cast a qualifying spell. It even works when an item says you cast one. #DnD

The Pathfinder Core Rulebook FAQ says that "you can't apply Heighten Spell to a spell at no cost: any increase to the effective spell level of the spell must be tracked and paid for by using a higher-level spell slot, above and beyond any other spell level increases from the other metamagic feats."

This means that a 1st-level magic missile spell that's modified by the feat Heighten Spell to a 2nd-level spell that's then modified by the feat Quicken Spell counts as a 2nd-level spell that requires a 6th-level spell slot.