You should probably stick with whatever drivers are available from HP for your system. Integrated systems graphics are not the best for gaming, but without knowing what your "weaker" pc specs are, it's near impossible to state what you be looking at for upgrades.
If anything, I'd probably look at upgrading your system RAM from 2GB to 4GB, but there is no upgrade for you graphics aside from newer drivers (if available from HP).
P.S. Sorry for the delay in responding. I've been offline for the last week.