So, just finished re-reading the whole thing and it's funny how your view on the characters shifts the second time around. The obvious core is Kodaka Hasegawa, our transfer student protagonist with the unfortunate delinquent look, and his neighbor and fellow 'loser', Sena Kashiwazaki. She's the rich, blonde, busty girl obsessed with eroge and sports games, but completely lacking social skills. They form the 'Neighbors Club' to try and make friends.
Yozora Mikazuki is the other founder, Kodaka's childhood friend he doesn't initially recognize. She's the brooding, manipulative one who calls Sena 'Meat' and comes up with all the disastrous club activities. Then you have the club members: the science-obsessed, robot-building Rika Shiguma, the petite and fiercely nationalistic Kobato Hasegaka (who's actually Kodaka's little sister and a self-proclaimed vampire), and later, the cheerful and surprisingly normal Maria Takayama, the nun-in-training who runs the daycare. The dynamics are everything—Yozora and Sena's endless feud, Rika's lewd jokes, Kobato's chuunibyou antics. The faculty advisor, Sister Kate, barely manages them. Honestly, the characters are less about deep development and more about watching this incredibly dysfunctional, yet somehow endearing, group fail at basic social interaction over and over.