According to Valve's list of requirements for Half-Life 2, a DirectX 7 level card is needed to run the game. While Nvidia's 8400 GPU is not geared toward gaming it will run Half-Life 2 fairly decently at medium graphics settings.
Some games may not run as smoothly on the nvidia 8400. I would recommend getting an 8500 if you have the money. If games do not run smoothly you can always lower the res and graphics of the game when you're playing.