I'd have to agree for the money the Lansky Turnbox crocksticks are great. They also have a diamond model for a bit more aggressive material removal, which you should be able to purchase in addition to the ceramic set for about $18. That plus shipping you're still likely under $40 for a setup that will do quite a bit.
I don't know much about the ZT 350 but from the pictures I found it looks like a recurve. I really prefer the DMT continuous surface stones (a set of C, F, EF would be within your budget), but I'm not sure if they would translate well for sharpening the recurve. Someone with more experience with both might be able to tell you.