really, there is no "best emulator".
depends on what you want to run.
if it mostly uses 3D, use No$GBA.
if it mostly uses 2D, use Desmume.
there are differences, and no$gba runs many 2D games perfectly or almost-perfectly.
but generally, it depends. just try both.
And P4 1.8 isn't fast enough for 7600GT Anything faster than 6600 (non-GT) is waste of money.
And of course it's impossible to run DS games at full speed on this machine, so real DS is a best option (compatibility of current emulators not good enough so new CPU won't help to make stuff more playable - some games are playable, but most of them not or have lots of glitches, it will take year or three to reach "GBA level")
This is one old discussion but for the future readers that will read this, I suggest this RetroArch Emulator for Nintendo DS. From my expereance, I will say that is much better that Drastic and No$gba.