The pink, yellow, blue and watermelon ball are played with similarly by the cats (animated).
The ‘pinpon’ ball however is a bit different so I would recommend it if you want variety. The cat uses its tail and right forepaw to play with it (animated):
The mocchiri ball (stress reliever) and capsule ball are played the same way as the baseball by normal cats, but the shape of the mocchiri changes while it’s being played with (animated).
The pink ball of yarn and soccer ball are played the same way (animated) as the temari ball by the normal cats. I think it’s just precious the way their legs move the ball.
So you should get:
Special items – baseball (for Tatejima San), temari ball (for Maromayu San)
1 of the normal balls, pinpon ball and the mocchiri ball shape changes a little while it’s rolling around so I guess it’s kinda cute.