What are the non game fish I can spear/bow fish?

It's easier if I first list the game fish.  They are all the trout species, all the salmon species, grayling, whitefish, cisco, crappie, perch, bass, all catfish/bullheads, sunfish, sturgeon, northern pike, tiger muskie, walleye, sauger, burbot, bullfrogs, and crayfish.  That essentially leaves you with suckers, carp, minnows, and chub.  Suckers and carp are probably the only nongame fish you see in shallow water in substantial numbers.  Look on the internet to see pictures of both species. I strongly suggest that before striking out on your own fishing with a spear or bow, you go with an experience archery fisherman.  They can show you where you're most likely to find carp and suckers, what they look like under water, and how to aim (water distorts your view of fish seen from the surface).  This can be a fun way to prepare for the fall archery season.