I loved Binbo Danshi!
Some stories with poor/ hardworking people:
-->Freeter, Ie o Kau (main character is a freeter but wants to buy a house for his family)
-->Yamada Taro Monogatari (Yamada helps his poor family; a heartwarming comedy)
-->Uta no Onii-san (main character has a lot of problems but learns to give his best)
-->My Girl (main character struggles to raise his daughter alone)
-->Bara no nai Hanaya (main character is really kind and works hard)
-->Shiawase ni Naritai! (Hikari gives her best to work for her family)
-->Bambino! (the main character works hard to achieve his dream)
-->SHARK / SHARK 2 (a band that struggles to debut and faces problems in the music industry)
--> Natsu no Koi wa Nijiiro ni Kagayaku (main characters work hard to achieve their dreams / for their family/ for love)
Also, Asadoras almost always have this theme. If you don't mind the length (156 episodes, 15 min/ep) you can try Gegege no Nyobo (about the life of the mangaka Mizuki Shigeru and his wife), Massan or Hanako to Anne.
