Zanjutsu, Hakuda, Hoho and Kido - the four basic forms of combat.
Zanjutsu is the art of Ōetsu Nimaiya. He is the inventor of Zanpakuto and it is more than logical that he is the best welder of this art.
Hoho and Hakuda are the arts of Senjumaru Shutara, she most probably invented the flash step. A tricky one, because as it was pointed to me by @Darestar, because Tenjiro was known as "Lightning-Fast Tenjirō" for his skill in Shunpo during his Seireitei days. But this means that shunpo was already there to use. Look at the Nianzol Weizol incident. Kirinji wans't fast enough and Senjumaru was. Also, we don't see her zanpakuto at all. Another thing that might be her ability is some kind of technical inventions. Her arms and ninjas seem to be mechanical.
Kido is the art of Tenjirō Kirinji and Kirio Hikifune. Reiatsu infused food is a Kido technique no doubt. Although I suppose Kirio relies on sheer strength when battling. Kirinji's technique also seems kido-based, more than that, his zanpakuto, which is directly connected to his soul is a paddle, pretty logical that his springs are his main thing.
Ichibei Hyōsube is most probably a perfect welder of all arts, an Aizen type of guy in a good way. I can't agree with Xil that Ichibei could be just the father of Hakuda. His name related to Ichigo's, the fact that his realm is the closest to the Soul King and his commanding tone to the rest of the squad may mean he is an ultimate fighter, based on the meritocracy of the Gotei 13.
It's just a working theory, what do you think?