Vampires are blood-sucking creatures from mythology and folklore all over the place, though I don’t (yet) know where the first vampires showed up…the modern iteration started sometime in the…17th century? I’ll have to check.
I personally think that Vampire: the Masquerade has the best vampire lore in terms of a cohesive story.
Buuut…I think that, maybe, Vampire: the Requiem actually does a better lore-job overall, though there are parts of Masquerade that are better. Requiem is at least better for mixing and matching.
Oh, right, half-vampires half-humans are called dhampirs.

I only heard of Underworld in reference to a lawsuit filed by White Wolf against it because they claimed copyright infringement in regards to the World of Darkness. It was settled out of court, though.
Underworld and Masquerade have very surface-level similarities, but are quite different. First, vampires aren’t dead…vampires are living creatures and specifically a sub-race of humanity.
They’re immortal, drink blood and can turn others via a bite…and, well, the sun hurts them. They’re also directly related to werewolves and exist in a vampire faction, similar to the Camarilla…I guess.
Though there is only one faction in this world…though, keep in mind that I only watched the first two films.
There’s also a worldbuilding issue in the sense that vampires cannot be descended from bats because vampire bats don’t live in Europe. The story there is that all vampires are descended from the son of Alexander Corvinus. This particular son was bitten by a bat, which is why they have their blood sucking abilities and the weakness to the Sun. Though, again, vampire bats don’t live in Europe.

This also includes the Chronicles of Darkness.
I consider the World of Darkness (Vampire: the Masquerade) to have the most definitive portrayal of the vampire. Not only does it account for multiple kinds of vampires, but it also has detailed lore on the history of vampires…as well as a lot of really good worldbuilding, like the Masquerade, which just makes logical sense.
That said, for the sake of inspiration, CoD is probably better looked at instead. It diverges more and has a sandbox-y nature to it, meaning you can better mix and match.

Okay so…my thinking is this: Masquerade has great lore overall. It all fits together neatly and the basic vampire lore is basically the gold standard…but when you get down to specifics, it starts breaking down a little. Like, the Toreador are the ‘sexy’ ones, for example, but they’re also obsessive artists. The lore fits, but it’s also so specific that it can’t really exist outside of Masquerade. However, Requiem’s clans are more generic (based on archetypes) which are more specific with Bloodlines. So the clans in Requiem are more malleable for further worldbuilding stuff.
Considering that, Requiem’s probably got the more definitive vampires since Masquerade primarily communicated the concept of clans, archetypes and the structure of the Camarilla (and the concept of the Masquerade) rather than…y’know, the specifics.

Vampires have a vested interest in using unequal (temporal) hours because they are defined as 12 day hours and 12 night hours. Since the times when night ends vary by day because of the positions of the Sun and Moon depending on the Season, temporal hours would be extremely useful, since you know exactly when the night starts and when it ends.