I'm sorry to ask this, I know it's homestuck 101, but why are the beta kids the betas if they came first? And which trolls are the beta trolls and why?

They’re the Beta Kids, literally, because of SBURB being a Beta. It’s not ‘Alpha and Beta’ as First and Second, it’s the Alpha and the Beta versions of the game.

As for the Trolls, Karkat’s group came first. It’s implied as such that Karkat believed the other group of Trolls was redundant, meaning that Karkat’s group was the original, cloned from themselves, and the Ancestors/Dancestors are their genetic offspring.

Let me take this moment to comment, however, that the Ectobiology Machinery in Karkat’s Laboratory has 24 vials for Ectoslime. Given that he doesn’t believe in Ancestors until he SEES the Dancestors, they couldn’t all be clones, which means… The Ectobiology machinery accounts for both Love and Hate Genetic Material.

Thanks, Troll Reproduction.