I suggest downloading 3D Mark 04 or 05 and test the speed of your gfx card from http://www.futuremark.com/download/.
 
Then you might have a better idea whats its capable of.
 

Most games don't perform all that well on a laptop. Sony Vaio's are a good case in point. Sony is quite proprietary and the drivers are often tweaked for performance for their machines. Nine times out of ten they are biased toward DVD and media presentations. Games are not a priority. You can take peterh's suggestion, but don't be surprised to find yourself coming back to this board wondering why your DVD is not performing adequately after installing a particular game.

You should be able to adjust the detail level in Quake 3 to be plenty acceptable for occasional playing. For much more, it will probably not have enough video memory.
 
Either way, try it, and let us know

Actually that should be a decent rig for a lot of fairly recent games. My dad has an old Gateway Solo 9300, it only has an old P3-600 with 256MB of ram and a shared 16MB graphics card. Of course he mainly plays the HOMM series of RTS's so there isn't a whole lot of power needed.
 
I also agree that the Sony Vaio's are tweaked towards DVD playback and presentations, however I still like and prefer an ATi graphics card for DVD playback
 
Also note that 3D Mark 2003/2005 are really geared towards the higher end desktop/notebook range of machines, basically 3GHz+ boxes with 512MB or more and higher end graphics cards.
 
I prefer to use 3D Mark 2001-SE for a better DX8.xx benchmark, this is most likely the type of games you really want to run on that machine anyway...