The three most important ones you'll want are Haiji's, Suzumi's, and Xeno's skills.
Shion/Tsubakura/Yabusame, Hooaka/Aoji/Kuroji, or Hooaka/Kuroji/Aoji are probably the best teams (in no particular order). Tsubakura/Shion/Yabusame is also pretty good, though the lack of range is sometimes noticeable.
For upgrades, I'd say Fumikado, Iyozane, Sukune, Hooaka, Jun, Kunimitsu, and Sanra are all good choices. If you're going with Shion/Tsubakura/Yabusame, Medias's upgrades are useful too.
For skills, you'll DEFINITELY want Xeno, Haiji, and Suzumi's. Also useful are Jun, Kunimitsu, Garaiya, and Mitori.
If you're playing as Shion/Tsubakura/Yabusame, get all of Shion's skills as well as Black Wings and Monochrome Ray Flash.
If you're playing as Tsubakura/Shion/Yabusame, get all of Shion's skills as well as Bird's Red Eye.
For the Hooaka teams, get Double Meaning, Aura Wind, First Rate Soul, and Insurance Bomb.