Feel free to go for 8” and 10” pans, but not 3” pans (for a taller layer), if you know what’s good for you !!!!! Charles T notes above you can likely make a 2” pan worth of batter in a 3” pan, but probably not an increased batch for a taller cake.
Actually, I haven’t used a 10” pan myself, but I think there are recipes in the wedding cake section for that size, so you can, no doubt, experiment with the “regular” recipes with, likely, good results.
You can try to just increase the batter, but I think you would probably want to adjust the baking powder (reduce it by, perhaps, 1/8 tsp per layer to make the structure stronger). The Rose Factor can likely help you adjust your leavening, also. You might have to use a flower nail.
I have used 8” pans many times. A recipe for two 9” layers works well for three 8” layers—there is a very light variance in the batter amount that you can calculate, but it works well without adjustment, also. You can increase baking powder by about 1/8 tsp. per 9” layer of batter, or you can bake “as is” and trim any domed tops.
Long story short, you’re definitely safe with 8”, probably safe with 10” (in fact, I’m sure others here have used them) ... but 3” pans for taller cakes are definitely risky!!!!!!!