The traditional classification of vertebrates is a mess, with a wide variety of paraphyletic groups that have either been abandoned or extended (here marked B). Unfortunately, no particularly standard system has settled in to replace it; the problem is there have been too many adaptive radiations. For now, here is a minimal tree of living forms including most traditionally class-sized groups:
Urochordata Cephalochordata Craniata Myxini (hagfish) Vertebrata Petromyzontiformes (lampreys) Gnathostoma Chondrichthyes (cartiligenous fish) Osteichthyes B Actinopterygii (ray-finned fish) Sarcopterygii B Coelocanthamorpha Dipnoi (lungfish) Tetrapoda Lissamphibia (frogs, toads, salamanders) Amniota Mammalia Chelonia (turtles) Squamata (lizards, snakes) Sphenodontida (tuataras) Crocodylomorpha (crocodiles, alligators) Aves (birds)
Information on characteristics of each group and a more detailed classification thereof should probably go under its headline - eg details of skeletal system and listing of jawless fishes under Vertebrata.