I got bit buy the sporting clays bug a few years ago. I had never shot a shotgun and when we went I hit 26 out of fifty. It was a small 50 round clays course. The gun I used was an old 870 pump with a fixed full choke. Depending on the choke you used changing it up may help.
What clays discipline did you shoot (sporting clays, trap, skeet, or 5 stand). A pump shot gun is a little disadvantage with a few of these since it is a little slower than a semi-auto or an over under. What helped me the most was going to the range and getting an experience trapper to pull for me. He shed a ton of light on how to lead different bird flights. It really just takes practice. The more you go the better you will get.
As far as the pump shotgun, use it. The guy that introduced me to clays shot a Benneli Supernova. He was an avid bird hunter and shot on average 40-45 of the clays on that same 50 round course.