The one nice thing I've found about HP is that they've got fantastic documentation online. Here's the
full spec sheet for that model. With a 250W PSU, and something that was likely meant to be budget, he'll need a better PSU with a PCIe connector if he wants a nicer graphics card. Granted, he's got Intel GMA 3100, so almost anything you can put in the PCIe slot will provide him with significant increases in performance.
Figure out his budget, then consult
this guide as a general what-to-buy. Granted, below the $90 mark, a PCIe cable won't be needed, and 250W
may be enough to power the system + new GPU. Just remember that adding that extra power does provide a
huge boost in performance, and considering the price differences in cards and the potential for extra gaming, it'd be a very tempting option.
Also, the 6770 can be found for less than $110-120 as stated in the article, often reaching
the $90 mark after rebates. In graphics alone, this is the cheapest card to provide 1080p at high settings, 60FPS in Skyrim. Not sure what the minimum CPU would be for that.