Monster Tinder

[Amaterasu]

Ash Williams

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Lamia!

Ash is, if I understand correctly, an undead time-traveler from the 21st century, with a robotic right arm with a chainsaw instead of hands, and who was brought to the 14th century by some enchanted book. That book also being the item responsible for his life having turned upside down, having made him undead and amputated his arm. Unfortunately that's not a lot to go on, but judging by that Ash had a girlfriend prior to the unfortunate chain of events, he really just wants a normal life.
The next best thing after a human girlfriend would be a Doppelganger, but - a monstergirl like that who will take on the appearance and memories of his girlfriend with a little idealisation on top, that's just too easy.
That's why Ash should try pairing up with a lamia. Why? Because of all monstergirls lamias are some of the most normal, if you discount their tail, and yet among the most adorable. A second-generation lamia, someone who has some experience with humans rather than never having seen one before would be better, as they have immense physical strength in their tails, and they like to use those. If they're not careful they could crush solid steel with it. A lamia that has been taught by her mother to be careful with this appendage around fragile humans will be a better fit.
Lamias are among the least monster-like monstergirls, they have mostly human instincts: unlike snakes they don't swallow live prey whole, they don't have venomous teeth and they don't even hiss. However they are cold-blooded, meaning that they will need warmth especially in the morning - meaning daily cuddles especially in the cold months -, they are carnivores and not the best cooks due to a weak sense of taste, so they'll have to share kitchen duty, and they are damn affectionate even when they don't need to cuddle for warmth. Oh, and they require a good bit of dedication in regards to housing, furnishing and such. If Ash doesn't like cuddly, snuggly girls, if he's a leg person or if he is scared of his girlfriend crushing him during a cuddle session, then he should try a Doppelganger instead.

Jacket

(Warning: NSFW)
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Nightmare!

Nightmares are a kind of rare subspecies of centaurs, which as its name implies sneaks into the dreams of its "prey", taking on various roles in those dreams and feeding from their spirit energy as they sleep. The particular Nightmare that I believe to fit best with Jacket is one that is somewhat older, more mature and that has developed a "second body". Because Nightmares' bodies are rather quite exposed when invading people the stronger ones transfer part of their conscience into a humanlike extension of themselves, which stays awake when Nightmare is in one's dreams and ensures that no outsider sneaks up on them. This, however, is not the reason why I believe that an older Nightmare would be the best fit. Young, adolescent Nightmares are far more interested in sexual interaction with their prey in its dreams to harvest raw, strong spirit energy, whereas the slightly older ones feed on the more subtle, soft and delicate spirit energy of those who can sleep peacefully and safely after having had recurring nightmares or not having been able to sleep due to fear or bad memories.
Jacket is a war veteran with a kill count so high that he stopped counting long ago, and suffering from PTSD. On top of that the "jobs" he's done for 50 Blessings keep him from finding inner peace even if he could deal with the horrors of war. Nobody, not even the most hardened soldier, can have a kill count as high as Jacket's and not be affected by it. This is evidenced by his smoking and drinking: ways to flee the world, to find refuge in something that numbs you and makes you forget. Similarly after his jobs he keeps meeting his former squad leader, treating him like a friend and giving him stuff "On the house" - the same words that the squad leader spoke while treating a half-dead Jacket -, another hallucination that is the result of Jacket longing for safety, warmth and someone to care for him.

But, onto the pairing. I don't believe that they should meet face-to-face... much rather, Nightmare will be drawn in by Jacket's ill dreams and bad memories, finding that such strong emotions would create a delicious spirit energy for her to feed on if she helps him. As said, Nightmare will want her "prey" to have good, peaceful sleep and to feel safe. To that end she will manipulate Jacket's dreams, shooing figures such as the masked people and the shock memories of people that he has killed from them and preventing nightmares from happening. Without rewriting his memories she will try to alleviate the horror, to help Jacket deal with the demons of his past. She will give him safety and warmth in those dreams, and care for him.
Eventually Jacket will find out though, as is the case with many Nightmares who overstay their welcome. He will notice that his dreams are shifting and notice traces of Nightmare's presence. That will be when they will meet. And strong as she may appear, she is a docile creature who will explain herself to Jacket. It is up to him to decide whether what she did is dabbling too much with his mind for him, or whether he is thankful for it. And if the latter applies, Nightmare, having spent so much time in Jacket's mind and having gotten to know him as a man who could be in a far better spot than he is, will be happy to stay. Granted, the influencing of his dreams may have effects for him in the long-term and Nightmare may demand that he quit smoking, drinking and wasting his life away, but she will more than make it up to him.
Oh, and remember how older Nightmares have two bodies? If ever things get physical, Jacket will have not just one but two lovely girls who both love him dearly.