Well the GTX 760 that I did suggest was actually 240 usd. There's just not much that's really interesting between the 760 and the 770, and AMD is pretty much out, at this price point. They got some great deals, on some other price points, but just not there. Last summer they had great deals on the 7950s, but now it's all gone, so your only good choices are on Nvidia, really.
Your PSU has two rails of 24A each, but they refuse to disclose how much they can deliver at the same time. It's good enough for the GTX 760, but I'm not sure about the GTX 770. It may work, but it's very close to the limit.