Is it true that the uglier the characters in an anime, the better off the it is? Like, is there a correlation to this? So, if the cast was nothing but fat, pizza-faced neckbeards it'll be a 10/10 in plot?
No, this is wrong.
But if you see that a show is decently popular, well-regarded, and has all (or mostly) ugly characters, that is a good sign. It lets you know that people aren't just talking it up because of cute characters or fanservice.
Yes, but that only applies to male characters. No one wants a story with ugly female characters.
Therefore, the best story would be one involving the ugliest male characters and the cutest female characters.
manga Kaiji is cute, no oily hair at least
Maybe something to take into account is that if the character design style is not cute and attractive, but the anime is popular, that means it's doing something very right.
For instance I think K-project is shit that just looks real sparkly and good, but it's not a good anime. People watch it on the account of "looking cool". As opposed to let's say Kaiji or maybe Ping Pong, where characters look unconventional, but the story is so so good.