As far as ingredients go, it really depends on the type of cake, so it's hard to give ideas beyond the basics (cake flour, vanilla extract, etc.) on that. Some ideas for equipment that's not included in your kit:

• Cooling racks - you probably already have these, but if not, tiered cooling racks are particularly nice for layer cakes so the layers don't take up a bunch of room as they cool.
• Bake-even strips - help produce cake layers that don't need leveling
• Cake lifter - makes it easier/less stressful to move around cake layers or a whole cake
• Cake circles (2" bigger than your cake. so I use a 10" circle for an 8" cake)
• Gel coloring for frosting - Americolor is good (and cheaper to buy from their website than Amazon, even with shipping costs). Make sure you have white and black so you can adjust colors.
• The right knife - you may already have a bread knife. If not, that or a slicing/carving knife is helpful for slicing or leveling cake. (I see your kit includes a leveler, but that wouldn't help with slicing, and slicing a cake is much more pleasant with a good knife as opposed to a butter knife.)
• Cake carrier - helpful not just for transporting cakes, but also for storing them in the fridge