After mozzarella, a fresh goat cheese like chèvre is a natural next step. After you conquer the basics, you may want to try hard cheeses such as farmhouse cheddar, Gouda or feta. There are plenty of recipes and kits that make it easy to jump into these more refined, aged cheeses.
Cheese wax
Your kit may or may not come with wax, so if you're making aged cheeses make sure you have some cheese wax to help preserve them (most people recommend having one to two pounds). Waxing cheese is a lot like making a candle with a piece of cheese: lots of dipping.
Start small
Even cheeses you can buy anywhere at the supermarket can take a substantial equipment and time investment to make. So start small and work your way up.