They're great if all you use are mostly business and internet applications with some light gaming. However, since you specifically stated that it's for game playing, go with a separate video and soundcard. Integrated video usually steals some system RAM and also competes with the CPU for RAM access. Separate video card have their own RAM and don't put this burden on the system's memory. Plus it's easy to upgrade the video card at a later time.
Integrated sound is usually just an on-board audio codec.
All of the sound processing is done by the CPU, causing an overall system slowdown. A separate soundcard, even a cheap one, does most of it's own sound processing, freeing up the CPU to do other tasks. This will run circles around ANY integrated video solution. I will use the computer for some gaming but mostly surfing the web and just maybe playing some games on the web. What do you think i should get now.