Opponent Lockdown: Dovescape, Rule of Law, Arcane Laboratory, Silent Arbiter, Teferi, Mage of Zhalfir, Ghostly Prison, Grand Abolisher, Grand Arbiter Augustin IV, Kira, Great Glass-Spinner, Cavern of Souls, Fatespinner- Self-explanatory. These cards are key for the functionality of this deck, since Bruna, Light of Alabaster entering the battlefield tends to set off instant alarm bells in my opponents. Teferi, Mage of Zhalfir, Grand Abolisher, and Cavern of Souls keep Bruna from getting countered when I decide to cast her, Arcane Laboratory and Dovescape prevent opponents from comboing off with their decks, Fatespinner and Ghostly Prison increase my longevity, and Silent Arbiter does the same thing but also increases Bruna's chances of hitting her intended target. Grand Arbiter Augustin IV is mainly in here for the two-mana discount for Bruna, but I lumped him into the "Opponent Lockdown" category mainly because I didn't want him to be all alone in a "Utility" category.
Auras: Angelic Destiny, Auramancer's Guise, Battle Mastery, Celestial Mantle, Corrupted Conscience, Daybreak Coronet, Eldrazi Conscription, Ethereal Armor, Spectra Ward, Steel of the Godhead- These are the main weapons in Bruna's arsenal. If we're being honest, of these Auras, the only three you really need to tutor up with Intuition or Three Dreams to seal the deal are Corrupted Conscience, Steel of the Godhead, and Eldrazi Conscription.
Countermagic: Mana Drain, Force of Will, Pact of Negation, Forbid, Alexi's Cloak (pseudo-countermagic), Mystic Veil (pseudo-countermagic)- I always try to ensure I have one of these at hand, in case someone wants to counter Bruna when I decide to cast her, remove her, or clone her after she resolves, and when I don't have Grand Abolisher or Teferi, Mage of Zhalfir on the field. While Alexi's Cloak and Mystic Veil are Auras, they can be flashed into the field in response to an Act of Treason or a Rite of Replication, so in a sense, they're partial counterspells.
Ramp: Expedition Map, Land Tax, Smothering Tithe, Weathered Wayfarer- Face it. Bruna is a 6-drop commander, compared to Uril, the Miststalker's 5cmc and Zur the Enchanter *f-etch*'s 4cmc, making her one of the most mana-expensive voltron commanders ever printed. As a result, we need ramp to be able to cast her earlier. Map and Wayfarer can tutor up one of the most important lands for this deck: Hall of the Bandit Lord, and all of these can get rid of late-game dud draws (Except for Smothering Tithe).
Sweepers: Cyclonic Rift, Cataclysm *list*, Tragic Arrogance, Austere Command, Winds of Rath- In order to be able to cast Bruna, I have to live long enough to do so. Therefore, control of the board is a must. My playgroup also has a tendency to play Avacyn, Angel of Hope, so I welcome any sweeper that contains the word "return" or "sacrifice".
Tutors: Heliod's Pilgrim, Three Dreams, Intuition, Enlightened Tutor, Idyllic Tutor, Academy Rector, Sovereigns of Lost Alara- Last time I checked, Bruna doesn't get Auras from your library (which is quite unfortunate). Therefore, I need to have tutors to put the Auras in my hand. Main ones here are Three Dreams and Intuition, since you can tutor up Eldrazi Conscription, Corrupted Conscience, and Steel of the Godhead and attach them to Bruna all in one turn.
Other Card Advantage: Compulsion, Compulsive Research, Epiphany at the Drownyard, Fact or Fiction, Frantic Search, Mirror-Mad Phantasm, Read the Runes, Rhystic Study, Sensei's Divining Top, Windfall, Traumatize- One thing all of these cards have in common (excluding Top and Study): they all involve putting cards in graveyards. One should try to discard only Auras, since they can be retrieved by Bruna anyway, while keeping a counterspell or a sweeper at hand should the situation turn dicey. The reason Mirror-Mad Phantasm is considered card advantage in this case is because it can dump Aura cards into the graveyard for Bruna to be able to fish back out and swing with.
Shroud/Haste: Swiftfoot Boots, Lightning Greaves, Hall of the Bandit Lord, Winding Canyons (pseudo-Haste)- As mentioned earlier, I would probably give anything just to give Bruna haste and hexproof. Because she doesn't have either of the two, I have to invest a decent chunk of my deck on cards that do so, such as the few listed above. While Winding Canyons doesn't give Bruna haste, per se, it can allow her to be ready to swing on my turn, so I put it in here.
Removal Protection: Gift of Immortality, Flickerform, Vanishing, Fool's Demise- Bruna tends to be a beacon for removal spells when she hits the field. Flickerform and Vanishing allow for Bruna to dodge sweepers and spot removal, and Fool's Demise and Gift of Immortality accomplish the same task, but I just threw both in to balance out the color distribution of the deck.