Try 1964...
Honestly, the big thing here is to look at other similar threads as this to find the best configuration of plugins possible for these specs.
As long as your Mario Kart rom is good, I see no problems why you can not run the emulator completely. As I use a Radeon 7200 pci on 1964 with no problems in this game.
One more thing...Your sound Card or Chip...What do you use and which plugin is configured for it.
Last point...This is a HP meaning it shares all and everything is shared by the memory...To lessen the effects of bad emulation...I would update video card drivers and sound drivers, maybe even running third party stuff, as the HP default stuff is just that (default)(generic)(Just to make it work) stuff. Other than that you have a box with a 2.8 GHz (ruffly 2.0GHz) for real world apps.