The Antec 300 is a great case with easy cable management, great airflow and plenty of space.
Corsair makes the best PSU's but you have to spend a bit more money. That OCZ doesn't even show the amperage on its rails, which makes it hard to tell whether or not it is substantially better. The Antec PSU isn't too bad, it most certainly isn't a piece of stuff.
The 5770 runs cooler than the 4870, has DX11, but isn't as powerful. That being said, the 5770 is the better choice, it will run anything you need. I normally don't roll with combos, but the one drbling posted is pretty good for a budget PC. The 500W PSU would be plenty enough to power a 5770 too.