First, many species have no direct “successor” but rather have branching some of which carries on, others that lead nowhere. The surviving fossils are only a part of the story. The nature of fossil formation and our discovery makes it kind of like reading a book from which most pages are missing. That said, many interesting fossils survive and are found so that we can look at numerous reptiles with “mammal” like adaptations. There are fossils of amphibians developing reptile like characteristics and of course, there are lung fish with lungs and gills and fins very much like legs. The horse is kind of interesting as we can follow its development from a dog sized herbivore to what they look like today.
My main interest is geology. In the last 200 years most of the current knowledge has been discovered or different interpretations have better explained old questions. We aren’t any smarter now as opposed to 200 years ago but we have a world more observations. Geophysics, structural geology and plate tectonics can now explain things that were only guessed at sixty years ago. We have satellite photographs and a good mapping of the ocean floor. We have worldwide systems to measure earthquakes and land movements. This gives us a limited ability to look underground and “ see” plate structures, magma chambers, fault systems not visible at the surface, and predict where we’ll find ore bodies, oil, gas, and see potential trouble spots.
I realize we all had these neat charts in our Biology classrooms showing the progression of the horse evolution from some small 'dog sized' critter to the 'Man O' War' horse of today -- but you realize that evolutionary chart was all wrong, right? Based on the 'fossil record', all of those critters apparently overlapped in their existence.
The 'fossil record' has been embedded with a lot of history of sleight of hand in an attempt to prove the 'macro evolution' model. A couple of key witnesses at the Scopes trial in the 1920s were the Nebraska Man and Piltdown Man. Just about 10-15 years ago National Geographic was trumpeting on its front pate some bird/reptile missing link that was found out in China. Around a year later, not on their front cover, they admitted they had been hoodwinked by some forgery.
Evolution across animal kinds is not going to happen. A winged bird is not going to 'evolve' from a land animal. Many of the requirements (hollow bones, feathers, two fully functioning wings, etc) would be an absolute detriment to the creature if it only occurred in small phases. A nonfunctional wing (or a single wing) would be a burden to the animal and set it up to be wiped out by predators.
There are many processes that cannot be reduced to single piecemeal partitions. Michael Behe's book, 'Darwin's Black Box', provides many examples from the 'simple process' of forming a blood clot, and the existence of the complex eye. All of these require multiple processes to occur at once. A single link in the chain would cause failure or death to the organism. The entire chain (or process) must be intact for the animal to survive. These processes cannot be explained by the evolutionary goo to you model.