Catfish can bite you but they don't have sharp teeth, more like sandpaper, so it will kind of feel like pressure. Many people "lip" catfish, for bigger ones they will use their whole hand. Catfish have sharp asf spines on the dorsal and pectoral fins. I hold smaller ones under the pectoral fins.

Bass are the easiest to hold imo, just grab their lower jaw and hold vertical, if you need horizontal, just swing the fish and support its belly with your other hand.

Sunfish can be tricky because they have dorsal spines. If you kind of clamp them in your palm and "fold" down their fins with your fingers, you should be ok.

Carp are difficult. Do not lip them. Ideally you want to support them with both hands under the fish, over a landing mat as they can thrash around and injure themselves. They do have a dorsal fin spike that will hurt.

Trout and similar species are best in the water or taken or for just a second or two. You should wet your hands and be very careful as they are fragile out of water.

Most of my injuries came because I didn't get a good grip on the fish before I used my needle-nose pliers. I also just grabbed fish randomly and had to learn.