Is there any way to make all of the planets normal sized planets (ex: no asteroids, or dwarf planets), save for the pirate base?
Yes. Make a map in the map designer where you use planet types that do spawn moons or asteroid (RandomTrue or the explict Terran/Desert etc. would work).
However, by default each homeworld has a "Starting Area" that includes asteroids and moons. To get rid of these, you'll need to save the map, then open it in Notepad and manually remove the asteroid and moon references from the starting area.