Capybara Normal/Water type. Make it bulky, and give it a lot of sleep based and support moves.
Super fast Electric type chipmunk. Non-Pikachu clone, though it's stats mirror them. Can learn seed based moves, and has Cheek Pouch.
A Fighting type rat that uses sticks to defend itself, and knows many forms of pole fighting martial arts.
Normal type flying squirrel with two forms. Full form gives it a secondary Ground typing, and it's ability is either Fur Coat or Thick Fat. Thin Form gives it a secondary Flying type with the abilities Speed Boost or Gluttony. It does this by either catching it in the wild or evolving it's first stage during a certain month. (Think of how Sawsbuck and Deerling work)
A few non-rodents, but small starter mammals:
Opossum with a Dark typing and Parental Bond (as it's covered in it's baby stage). Learns many multi-hit moves.
Normal/Flying jackalope that uses its ears like wings.