Before you buy anything
A few things worth knowing first
Cold brew and iced coffee are not the same thing. Iced coffee is hot-brewed coffee poured over ice — it's thinner, brighter, and more acidic. Cold brew is steeped cold the entire time, which produces a smoother, sweeter concentrate with about 70% less acid. If you've had bitter or harsh cold coffee in the past, this is the method that changes your mind.
You're probably making concentrate, not ready-to-drink coffee. Most cold brew recipes produce a 4:1 concentrate — one part cold brew to one part water or milk to serve. If you drink it straight and it tastes intense and overpowering, that's correct. Dilute to taste. This also means one batch goes a long way.
Grind size is the only real technical variable. Too fine and you'll get bitter, silty concentrate. Too coarse and it'll taste thin and weak. You want coarser than anything else you'd brew — think sea salt, not table salt. This is the single adjustment most beginners need to make after their first batch.