Changshi the Spiridao

1. She can send 1 zombie monster from the deck or hand to grave. Most of the times you'll send either Loading... or Loading... but there will be times where you will send different cards.
2. If she is banished you can banish a zombie monster from your grave to summon her. Keep in mind that now she won't go back to grave after being removed from the field, instead shuffling herself back into the deck.

Arguably the most important card to have come from the Structure Deck. The ability to mill any Zombie-type monster, while not exclusive to Changshi, is just as important here as it is on any card. The cost of banishing a Zombie from the grave to bring herself back is circumvented elsewhere in the deck making her a free Special Summon in essence.

Samurai Skull

1. When this card is Normal summoned, send 1 Zombie-type monster from your deck to the grave.
2. If Samurai Skull leaves the field because of an opponent's card effect it can Special SUmmon another Zombie-type monster from deck

Samurai Skull is your best possible Normal Summon. The combination of activating its effect on Normal Summon and actively punishing the opponent for using removal (that isn't a spin) would be valued in a starter by just about any deck out there, let alone a deck with the amount of extension this one provides.

Uni-Zombie

1. Target one face up monster on field increase it's level by 1, then send 1 Zombie-type monster from deck to grave, if you use this effect you can only attack with zombies), doesn't come up often but important to remember.

2. Target one face up monster on field increase it's level by 1, then discard 1 card from your hand.

Another option for the Normal Summon as it ultimately fills the same role as Loading... , but not preferred for reasons listed for Samurai Skull. It being a tuner monster can come up for specific lines but generally doesn't come up.

Mezuki

1. You can banish this card to target 1 Zombie-type in grave and Special Summon it.

Strongest single card not only in this deck but for any zombie deck in general. The best thing about the card isn't whats on the card but what isn't, that being a hard once per turn clause. Already a devastating fact on its own that's only made better (or worse depending on your view) by another card to be mentioned.

Mad Mauler

1. While it is in grave you can target a level 6 or higher zombie on your field, lower it's level by 2 and then Special Summon mauler from grave. While it's on field you are locked into zombies.

Mad Mauler is your main target for Spiridao to send off her effect for being able to better establish the grave with more Synchro Monsters and provide an extra layer of follow-up.

Shinobi Necro

1. If another Zombie-type monster is Special Summoned while he is on field you can draw 1, then discard 1 card.
2. If he is banished from the grave you can special summon him to the field, but banish him when he leaves the field.

The main utility in running Shinobi Necro is the ability to better play around Loading... than Mad Mauler. Past that it's entirely up to preference.

Alghoul Mazera

1. If a Zombie-type monster you control would be destroyed, you can banish Alghoul Mazera from grave or hand to protect that monster from the destruction.
2. If Alghoul Mazera is banished from hand or grave you can Special Summon Alghoul Mazera and can choose if you want to make him lv7.

Red-Eyes Zombie is already resilient to traditional forms of interruption, more so than other decks, so having a card with the potential to nullify one piece of disruption feels like a no brainer. It's ability to Special Summon itself on banish can help extend certain combo lines as well.

Gozuki

1. During the Main Phase you can send 1 Zombie-type monster from the deck to the grave. Nice and simple.
2. If Gozuki is send to grave by any means you can banish 1 other Zombie-type monster from your grave to Special Summon a zombie from hand.

Something important to note is that, under the skill's restrictions, Gozuki cannot be Normal Summoned. However, it can still be Special Summoned which allows you to utilize the card in certain lines. That being said it's another pure preference card as its not at all necessary.

Glow-up Bloom

The only relevant effect is

1. When this card is sent to the grave you can add 1 level 5 or higher zombie monster to hand.

Makes both Uni-Zombie and Samurai Skull a 1-card combo by adding Loading... to hand, you might want to play it but I don't think there is need to.

Burial from a Different Dimension

This card is another big reason to why the deck is as strong as it is. The card allows you to return up to 3 cards from banishment to the grave. The cards in question for this deck will almost always be used copies of Loading... . Seeing this card can make the different between a board your opponent can crack versus one they can't, a hand that can play through your opponent's board versus one that can't.

Zombie Reborn

You get this card from your skill so no reason to play it, but it still warrants being talked about. It lets you revive one zombie from either grave, but you need to banish a card with the same name from your deck or extra deck. There is also a 2nd effect that comes up in grind game, allowing you to return 1 banished zombie to the deck to set Loading... on your field, keeping in mind you can't use it until next turn.