The closer your sugar is to white refined sugar, the better your recipe will work. Unrefined cane sugar and demerara are both quite good choices. They just have a tiny bit of molasses, else they are almost the same thing and behave very similar to white refined sugar.
Honey has a lot of water, around 17%. The same goes for many other syrups (date syrup, agave syrup). Changing a recipe to work with those will need a lot of experimentation, costing you time and materials. I wouldn't recommend doing it. You can try finding a recipe developed with those in mind.
Other sugars such as pure dextrose or fructose also won't behave the same way as standard white sugar, even though they have no water content. You'll need new recipes for them too.