Depends on the needs, low power consumption, 4770, slightly better preformance, 4850, better performance at higher resolution, 4850 1GB because there is no 1GB 4770.
It does require a PCI-E connector so you will need a reasonably modern power supply but any decent 400 watt and up power supply will have enough for it.
It depends on your needs, when i built my system the 4770 was more than the 4850 for lower performance so i went with the 4850, but if you were going to be putting it in a place with limited cooling or power options or need quietness i would get a 4770.