Arcade emulation is a confusing beast when starting out.
Basically ROMs will only work for specific emulator versions. For example, Mame 2003 needs roms from the 0.78 romset. You need a corresponding BIOS file for the same romset as well (neogeo needs to be correct version. This was my downfall for a while with neogeo games)
Familiarize yourself with the different arcade emulators in Retropie and what kind of performance and compatibility you can expect. You need to note the versions of each emulator. Then ensure you have roms from that version's romset.
For what it's worth, so far I have stuck with the FBA emulator. It's got good compatibility and performance. Note that generally speaking, the higher the accuracy of emulation, the worse the performance....