The best DeSmuMe emulator is 'DeSmuMe'. Of cause there are the JIT, SVN, X432R, and the original version releases. Personally I'd prefer the SVN release.
Use version 0.9.9 for safe mode if version 0.9.10 and latest SVN have problem with some games. Also, is some games have trouble with using JIT feature (likes missing some screens, game crash etc), turn off it.
Its "BEST" to use multiple versions of desmume since it varies and some versions wont play games properly. also its in your best interest to use no$gba/zoomer also for those just in case.