Allow me to preface this deck guide by saying that Vampires are by no means competitive, so this is my best attempt at a competitive list. Side deck options will vary greatly depending on your match-ups, so tweak the side deck to suit your specific situation (i.e. I didn't really know what to put so I filled it with staples and some decent alternative cards for the deck). For this guide
I will bold hypothetical combos to provide an example of some things you can do with the deck. If you'd rather figure it our for yourself or just know the deck well enough already, ignore those bolded portions.
This deck likes to go first as you run several powerful floodgates in the form of Rivalry of Warlords and Zombie World, as well as have access to a strong omni-negate counter trap with Vampire Domination. Doomking Balerdroch is also far better used when going first to prevent your opponent from setting up. That said, the deck
can also go second somewhat thanks to Doomking's ability to break boards and the inherent ability of Vampires to hit things real good (as well as Vampire Red Baron's creature swap effect).
The main goal of the deck is to open a combination of either Uni-Zombie or Shiranui Solitaire and Glow-Up Bloom, Necroworld Banshee or Zombie World.
Opening Uni-Zombie and Glow-up Bloom, for instance, will allow you to pitch Necroworld Banshee from deck to get Zombie World and then discard Glow-up Bloom to summon Doomking Balerdroch (AKA standard Zombie World Control stuff). Obviously what you pitch from your hand/deck will depend on your exact opening hand. This is your primary combo and is what you want to be aiming for if you can help it. Handtraps ruin this combo so Called By the Grave is a mandatory 3-of to counteract the Veilers and Ashes that will be thrown at your poor Uni-Zombie. 1 copy of Gozuki and Foolish Burial provide potential alternative combo starters should you fail to open Shiranui Solitaire or Uni-Zombie, though they require more specific opening hands to fully access Zombie World and Balerdroch. Other ways of accessing the combo exist,
such as normal-summoning Glow-up Bloom with Zombie World up and making Linkuriboh to summon Doomking Balerdroch from the deck. Often a "completed" Zombie World play will end on Uni-Zombie and Doomking Balerdroch, which you can then link away into Vampire Sucker as Balerdroch will summon back from the grave on the following standby phase, netting you a draw off of Sucker.
The standard Zombie Synchro play is still possible here, enabled by a single copy of Gozuki. The only level 8 Synchro I'm running that you can make off of Uni-Zombie, Shiranui Solitaire and Gozuki alone is Psy-Framelord Omega as I've never found another level 8 to be worth it (without links in the grave for Borreload Savage Dragon), but other options are possible. I am also running a few fusions with Super Polymerization in the side deck for extra removal if you have to go second. You could main-deck Super Poly if you so choose as it's very good with Zombie World up, I just find it to often drain your hand at inopportune times.
The addition of Vampires somewhat complicates things as they both provide you with alternative opening plays while also occasionally clogging your opening hand. Often, if you fail to open the full Zombie World "combo" you can instead divert your attention toward the Vampire portion of the deck instead. If you open a way to discard or mill any 1 monster you can typically access a Vampire combo, although the specifics will depend on your exact hand somewhat. The main goal of Vampires is to put bodies on board and hopefully end up with a Synchro or XYZ monster to suit your purposes. While the deck wants to go first, Vampires are awkwardly stuck in a position where they both want to go first to set domination and avoid their weird battle phase restrictions while they also want to go second to steal/tribute the opponent's monsters and generally break boards and gain LP. There aren't really many defined Vampire "combos" and what they can do is largely determined by your exact opening hand, but I'll attempt to provide a sample combo for reference:
A Vampire-capable hand would be something like opening Uni-Zombie, either Vampire Familiar or Retainer and at least 1 other Vampire card to discard. Opening Uni-Zombie, Vampire Familiar and Vampire's Domain for instance would allow you to mill Vampire Retainer off of Uni-Zombie, activate Vampire's Domain (and use its effect for an additional normal summon), then send Familiar from hand to the GY to summon Retainer from the GY using its effect to search out either Vampire's Desire, then send the face-up Vampire's Domain to the GY to summon Familiar from the GY and search Shadow Vampire off its effect. At this point your field will have a face-up Uni-Zombie, Vampire Familiar and Vampire Retainer (both of which will be banished when they leave the field), with at least Vampire's Desire and Shadow Vampire in hand. You could potentially go for a level-8 Synchro play here if you so desired. Alternatively, activate Vampire's Desire to mill any desired Vampire you wish to summon from the GY (either Fraulein or Red Baron, depending on if you'd like to go for an XYZ play or not), then link any two monsters into Vampire Sucker and use your additional normal summon from Vampire's Domain to tribute the third monster for Shadow Vampire. Off of Shadow Vampire, summon Vampire Scarlet Scourge from the deck, which will trigger to special summon whatever Vampire you milled earlier (either Fraulein or Red Baron), and Vampire Sucker will let you draw a card. At this point your exact ending board will depend somewhat on what you decide to go for and what the two remaining cards in your hand are (a rank 6 XYZ for instance, like Beatrice, Lady of the Eternal can allow you to extend your combo and potentially get out Balerdroch/Zombie World depending on the two unused cards in your hand).
This deck has a ton of level manipulation, which enables you to easily make Synchros with a variety of hands. I run a decent Synchro package of level 7's and 8's as those are the easiest to make in the deck, but you could theoretically make Synchros of any level with this deck thanks to the wide variety of levels, tuners and level modulation of Vampire's Desire and Uni-Zombie. Obviously other links could be played as well, though I find the ones I've listed to generally be sufficient.
The Zombie World support and Vampires do have a great deal of synergy that is worth noting. Having Zombie World up on the field allows you to tribute any of your opponent's monsters for your tributes so long as Vampire Sucker is on the field, which comes in handy surprisingly often in longer games and lets you easily get around problematic monsters. Glow-up Bloom also lets you search (or special summon with Zombie World up)
any level 5 or higher Zombie monster. This means you can search out or summon Vampire combo pieces as well, mainly Vampire Scarlet Scourge or Shadow Vampire (Fraulein can also be searched if you need to beat over something big). Vampires allow you to make big boards and do lots of damage while sustaining yourself, while Doomking Balerdroch and pals give you a somewhat more consistent goal to reach for and offer an insane level of control thanks to the sheer power of Balerdroch (with Zombie World up, of course). Part of the beauty of this deck is its versatility, as no two games will ever go the same way. Unfortunately, while this variety is the deck's most entertaining element and makes it extremely fun to play, ultimately the unpredictable nature of the deck results in poor consistency and easily-interruptible combos.
TL;DR
The main idea of the deck is to go first and be annoying, but going second is also possible. Your primary goal should be aiming for Zombie World control status (Zombie World up and Balerdroch in play). Vampires can extend plays beyond this point depending on your opening but are more hand-specific and should be regarded as secondary to the primary goal. If the primary goal cannot be achieved using your opening hand, aim to end on whatever board is possible given your opening, whether that be Synchros or XYZ monsters.
This deck isn't very competitive but this list is what I've found to work best against a wide variety of decks of varying power levels. Good luck and have fun!