The API Master Freshwater liquid test kit is the way to go for sure! It tests for ammonia, nitrite, nitrate and pH. It can cost anywhere between $25-50, but there are over 700 tests in eash kit so it's worth it!
Also, alot of us on here use Seachem's Prime water treatment, which removes, cholorine, chloramine, ammonia and helps neutralize nitrites and nitrates. I am not sure about a test for chlorine, but I don't worry about it because I use the Prime.