Extra Deck:
The Extra Deck is rather subjective, as D/D can access any of the extensive options in the Rank 8 toolbox, as well as being able to use their own fusion monsters fairly easily.
D/D/D Flame High King Genghis
Flame High King is a PHENOMENAL card when going against backrow, allowing you to just ignore any one spell or trap during each of your turns. He also revives any D/D monster when another is summoned to your field, and just so happens to be Level 8. He is, however, currently hard-limited to 1 copy via level-ups.
D/D/D Dragonbane King Beowulf
Beowulf is an OK card. He provides every D/D monster on your field (including himself) with piercing damage, and allows you to blow up all cards in the spell/trap zone during your standby phase. This is good for baiting out backrow at the start of your turn, and also allows you to dodge the damaging effects of your Dark Contracts. He's also an 8, which is always nice.
D/D/D Oracle King d'Arc
d'Arc simply converts all effect damage you take into free LP. This circumvents the downside to your Dark Contracts, as well as any damaging effects your opponent may or may not be running (yubel). However, his awkward level means he tends to clog your field after he's served his purpose.
D/D/D Super Doom King Dark Armageddon
Besides being a mouthful, Dark Armageddon is D/D's own Rank 8 Xyz monster. He protects all Pendulum Monsters on your field from destruction effects, and can detach one material to destroy a number of monsters your opponent controls equal to the number of pendulums you control. This must be EXACTLY equal, however rather than up to the number you control. This, along with the fact that he requires two D/D/D monsters and so cannot be summoned using Thomas, means that he is often rather underwhelming.
Divine Dragon Knight Felgrand
Felgrand is one of the only Rank 8s that provide interaction during your opponent's turn. At the cost of one material, he can both negate a monsters effects and make it immune to card effects until the end of the current turn, meaning he can be used both offensively and defensively. He is currently hard-locked to 1 via a special bundle, and also at 1 on the banlist, meaning he clashes with the next monster on this list.
Coach King Giantrainer
Giantrainer lets you draw 3 cards. That's it, besides maybe a bit of effect damage. You use him to dig through your deck to find your generic backrow, and to refill your hand for next turn. Due to him being limited 1, you will have to choose between running him or Felgrand when you construct your deck.
Dingirsu, the Orcust of the Evening Star
Dingirsu is a solid monster. He's non-targeting, non-destruction removal on summon, meaning he works on the vast majority of threats. In addition, he protects your first two cards to be destroyed by battle or card effect. Very good if you can get him out first turn with felgrand, or when used going second to clear boards.
The Galaxy-Eyes Engine
Galaxy-Eyes Cipher Dragon, Galaxy-Eyes Full Armor Photon Dragon, and Galaxy-Eyes Cipher Blade Dragon are played as a set. By ranking one up into the next, you can destroy 2 cards on the field, ending on a monster that floats back into Cipher Dragon upon destruction. Definitely worth the 3 spaces
Number 68: Sanaphond the Sky Prison
Sanaphond is a more niche option, being better against some decks more than others. Locking certain decks out of summoning from the graveyard can be devastating, making him entirely matchup dependent.