summoning pets are not class based, but rather very team specific, since they work as links that help to create higher combos.

Test your team on the simulator with different summoning pets to see which one will work the best.
http://*.qq.com/tool/huoying/mnq.htm

gold > purple > blue in terms of their stat bonuses and chase effects

or try this one
https://narutobb.gm99.com/huoying/mnq?game=huo
this is the taiwanese version
there are no other ones

even if it does not always show the right effects,
you can still get a general idea for combos