Sincerely, if you don't plan to invest in, at least, a single 4890, your build will not be able to render today games.
A 4670 is a HTPC card that I don't recommend at all for gaming purpose.
You don't need a Phenom II for a good built, but you should sincerely think about it. If not, go with an Athlon II X4 620, a nice chip.
If your goal is having a simple PC for browsing the internet and watching movies (or shows), I would suggest you to invest in a cheap motherboard using an IGP (Integrated Graphic Processor). That way, no need to buy a video card.