You bought a 3x2GB RAM kit, but AMD uses dual-channel, not triple-channel; you wanted a 2x2GB kit.
You don't have a CPU fan listed, so I am assuming you plan to use the stock fan, with minimal overclocking. You won't need the cooling of a premium case, so I'd look at the less-than $50 Rosewill offerings. If you want to spend a little more, look at the Antec 200 or 300.
AMD says a 500W or greater PSU should be used for a single HD5830. If you are planning on adding another HD5830 for Crossfire, get at least 650W. Choose a quality PSU with full range active PFC (no little voltage switch) and 80+ certification. Antec, Seasonic, Corsair, and Enermax are among the quality brands.