Impressively.
But you did forget to mention the sort of 'bloodline' of the vampires on the show.
Way back before things like electricity or America, there was a female vampire named Darla. I missed out on the really old part of the backstory, but long story short, she turned a normal ho-hum chap with a bad Irish accent into a vampire. This was Angelus. What you need to understand from the get go is that in the Buffy/Angel universe, vampires and various other nasties don't have souls. If a person is turned into a vampire, he keeps his memories, but loses all traces of humanity and remorse. Vampires simply aren't 'good.' You can stake them all you want and not feel bad about it, because they are just forces of evil (that happen to get all bumpy on their foreheads for some reason).
Jump forward a long span of time, as Darla and Angelus travel around England having violent and bloody fun.
I think Angelus turns Drusila into a vampire. Drusila was just a waifish young lady who apparently had second sight, which is why she always seems a little out of it. Drusila, in turn, decided that she wanted a boytoy vampire, and she chose William, a poet who some people called 'William the Bloody' because his poems were so bloody awful. She turned William into a vampire, and later he changed his name to Spike because he got into the habit of stabbing people in . . . the head? with railroad spikes. That was in the 1880s.
Some time around the turn of the century, Angelus, Darla, Drusila, and Spike are roaming around central Europe, wreaking havoc, when they come across a group of gypsies. Angelus has his fun with a gypsy woman, and kills her. As punishment, the girl's father places a curse on Angelus to give him his soul back. This comes with the disclaimer that if he ever experiences a moment of true happiness, he will lose his soul, and revert to his nasty vampireness.
Angelus changes his name to Angel, and with extreme amounts of angst, leaves the group of vampires. He has trouble surviving as a blood-sucker, and tries once to go back to Darla and the gang, but he can't bring himself to be evil. This is around the same time that Spike kills his first Slayer, during the Boxer Rebellion in China.
Some time between Angelus becoming Angel, and the 1980s, all these vampires make it to America. Spike bleaches his hair blonde and kills another Slayer in New York. Angel moves around, living off rats and slaughterhouse blood. Then, . . . and here's where I get pissed at myself for missing out on season two of Buffy, Angel gets a new lease on things, and decides to try to actively be good, tracking down this new Slayer, Buffy, and falling in love with her.
Then, between Season Three and Four of Buffy, Spike turns Harmony into a vampire. Why, I have no idea. Apparently the writers wanted an immortal ditzy blonde for comic relief, to torment us forever.