Actually the integrated Radeon 4200 is a pretty decent little onboard graphics choice. It's integrated in the 785g chipset, and it can actually do some light to moderate gaming. The Radeon 4200 will run Left 4 Dead at Medium settings and 1280x1024 at between 40 and 50fps!. It will even run Crysis at low detail and 1024x768 at around 30fps!
I know these numbers are small, but it's one **** of a powerful integrated* graphics solution.
I would recommend AGAINST the 4650, because the 4670 is quite a bit more powerful, and only a few dollars more expensive. I used a 4670 for my nephews computer, because I knew that I could just set the games at 1280x1024 or 1600x1200 and he wouldn't notice the difference, and the 4670 chews up any game he plays on it.
If you want to save some money, and do some light gaming for a while, look in to an AMD solution with a 785g chipset. The Athlon 2 x2 240 is cheap, can be found in many combo deals, and paired with a 785g you would have a decent little starter platform.
EDIT: I just re-read through this thread to check to see if I was repeating something someone else already said, and it turns out I was!!!
I Highly recommend the build Trotter put together for you, it will run any recent game at low/medium details, and many older games with high details. Not to mention you'd have excellent options for upgrading in the future