Dedicated graphic/video memory question

I am slowly getting tired of working exclusively on a 13" laptop. I feel like I need a bigger screen and a more snappy hardware.

While I am not sure I really need the latest Core i7 8GB RAM systems that are available in retail stores for the work that I do, so I am out looking for a refurbished PC that has the following specs:

AMD Phenom II X4 820 2.8GHz <-- is it any good? is it quiet?
6 GB RAM
Integrated ATI Radeon HD 4250 graphics

The problem is - it sounds like there is no dedicated video memory on the machine, compared to those i7 8GB RAM system which have 1GB of dedicated memory.

So, with the above specifications, do you think there is a possibility to set/modify/apply a share of the overall RAM toward the dedicated graphics memory? I am really not strong on the hardware subject of things, so would appreciate a smart advice.