Hm, this post made me check something...
And really it's interesting that both the Hellsing anime and OVA take different approach than manga in the first scenes.
And... I actually like the original manga better in this way.
[warning: basic Hellsing spoilers in the text]
The old anime (which had a lovely and original art style btw. And they were sooo good at drawing teeth 🤩) starts with a new, non-manga scene immediately, where a man is almost tricked by a vampire, when a mysterious man in red appears, mumbles some kind of technical nonsense (release power level...), takes out a gun and shoots the vixen, who turns out was a vampire. It is also - by Alucard's smile - before even the shooting revealed he's a vampire too, and he's all dark and condescending and what not. So... yes, it establishes right away the kinda detective theme this series has. You know that there is an ultra cool, smug and probably powerful dude who'll be handling interesting cases.
The first view we get of Alucard in the Hellsing series:
The OVA, that starts with one of the most emotional and cool moments of manga, where small Integra is running for her life from her uncle who chases her with a gun to dispose of her - so he can inherit the Hellsing estate. She is seeking help in an old abandoned prison according to her dying fathers instructions. However she only finds a dried corpse... which turns out might not be only a dried corpse, when it's woken up and kills the guys with the guns. Then when we're back in England present day, for the hunt of the vampire priest - same as the start of the manga. We have a view on Alucard, and he looks at the moon, smiles with the vampire teeth and says that nights like this make him crave drinking blood.
My overal feeling from this: a fucking cool vampire, he's gonna be a menace, yeah the priest doesn't stand a chance.
The first view of Alucard we have in the Hellsing OVA:
The manga... Maybe it's the more goofy style of art, but... How it starts invoked in me different feelings, like: this is a strange guy. But he doesn't look much like a menace. He's not even focused on the mission properly. What the hell is going inside his head? How will he handle it? My reaction is quite the same as the guys from the police when integra tells them: I've sent only one person. Like: what?? hmm, he must be strong. But then you see him and you're like: what. This one?
When he looks at the moon he says: nights like this make THEM crave drinking blood. (or at least in the translation that I have)
And then only waay later, while it seems the priest has killed him, you find out that he's also a vampire. And you go: okay, he's actually cooler then I thought. And then as the story goes you're more and more intrigued because your first impression of him was so different, there are revealed more and more dark secrets, culminating in the end when you find out what he really is. It makes you go through so many layers. Alucard is a very layered and complex character. And I love that at the start of the story about the most powerful vampire in the world your first thought is: well this is some strange steampunkish distracted weirdo in clothes too big for him, who looks 20 and not like a menace at all.
As you've posted here, this is he very first view of Alucard we see in the manga: