Frankly, for Megadrive emulation I prefer Md.emu. I don't like the way sound is emulated on Picodrive, sounds a bit tinny to me. Plus, some games just seem to play better on Md.emu, I don't know why. Oh, but don't even think about playing Sega CD games on Md.emu! It has some game-breaking bugs, so for Sega CD and 32x you stick with Picodrive.
PCSX is as awesome as it gets on the handhelds, but be aware that I doesn't emulate everything perfectly. Earlier Ridge Racer games are kinda slow (RR T4 is fine, though), and some random games like Crusaders of Might and Magic are really unplayably slow. But I think that most good/important games work perfectly fine.
On the matter of GBA I offer a second opinion: use Gba.emu. gPSP is prone to random crashes in some games. It is much faster, but if you have a Ghz unit you should have no problem overclocking your Pandora slightly, which will solve the speed issue with Gba.emu.
Mupen is an adequate N64 emulator, but nobody should ever emulate N64 on the Pandora because of the evil nubs which will fail eventually and are generally unpleasant (there is a rumor that after failing they can become sentient and may occasionally insult your mother).
PCE.emu is a superior way to emulate PC engine, I suppose. The other viable option is mednafen, but PCE.emu has much nicer interface.
NES- stick with GPFCE.
SNES - 9x4p. It is MUCH faster than Snes9x EX and is generally better in most ways. Some games (Super Ghouls n' Ghosts) have minor glitches related to transparency, but Snes9x EX is having trouble running some games altogether (Kirby superstar, which runs perfectly on 9x4p).
As for home computers, I think all emulators are good. I prefer C64.emu to VICE because it has easier interface.
GB/C - Gambatte. It's very good, although its interface is a bit odd.
MAME - I'm using MAME4ALL. I know it's old but I don't like fiddling with romsets, and I already have 0.36 romset ready, so... Anyway, it plays all the ancient arcade games perfectly and requires zero fiddling. But I suppose you should try Panmame if you're ok with grooming your romsets for it.
DraStic is an excellent DS emulator.
PPSSPP doesn't really play anything for me, but I have a Rebirth Pandora, so maybe you'll have better luck with it.
Oh, there's also Mednafen, which includes many emulators... I personally would recommend its Atari Lynx emulator. It's fiddly at first but emulates that system perfectly as far as I can tell.
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