No one word answers!
ehem...I mean, please explain your choice, thank you.

If you are into emulation and willing to softmod it, the PSP can't be beat imo.

They are relatively cheap now if you get a good quality used one. Plus softmodding lets you copy your UMD games to the memory stick so you save battery life and don't have to haul them around with you. The system has a good library of games to pick from cheap now also.

If you only want to pick from current active systems, I'd say a 3ds. The Vita isn't selling well and with Sony having to focus mainly on the PS4 launching this year, it doesn't seem to be getting much help to stir up interest again. Also the prices for the proprietary memory cards are stupid.

Depends on what you're looking for and what type of games you want.
The Ps Vita hasn't got much games yet but is the most powerful handheld ever. The 3ds is kinda disappointing compared to the DS but newer games mostly don't work on DS so...if you like nintendo games / the licenses they have you're pretty much stuck with it.

The best handheld ever is the neo geo pocket color though. You can probably find that really cheap.
My opinion of course ;)

Overall, the one i feel is the best choice right now if you don't own one, is the PSP. The DS is a good choice if you want some of the games that are only on that system (jrpgs ? like dragon quest/final fantasy games).
You can also have some emulators on DS, even though a fewer selection than on PSP.

I love my modded PSP. It's definitely the way to go. The portable has a great selection of games as mentioned above, including some nice japanese rpgs (Persona 2-3, Final Fantasy Tactics, Tactics Ogre, Lunar Silver Star Story Complete etc) and compatability with just about every Psone game. It's also good for pretty much any other emulation you can think of (up to Psone)... GBA,Snes,Megadrive,Master System, Neogeo etc etc etc.

Edit: I used to own a DS but it wasn't very good. GBA was but you're better off emulating it on the PSP tbh.

The DSLite probably still has the best library of titles available and it's the last handheld without region lockout, so yep, you can import games on it if you like. However certain types of games are probably better played on something like a PSP or Vita, still, DSLite is probably the easiest to recommend due to its massive library, extremely low price, good battery life, and lack of required extras (though I'd recommend a second charging cable and a carrying case that zips up and holds a few games).

Please no emulations, I'm anti-piracy sorry.

PSP if you want hacked stuff (not Vita) 3DS if you want new games (because the Vita ain't doing too well for games at the moment). The Vita might pick up later on, but there's no guarantee. While there can be links between the two, emulation =! piracy. :P

Shame on you, Anne Bonney was a legend.

and it comes in pretty colours doesnt it? ;)

Mine is pink!:)

The PSP is probably the choice for emulation, heaps of older games library. As to which model PSP1000,2000,3000 (try not get the GO - thats pretty much a download only missing the umd drive i *think*)....

Treated as piracy by nintendo though :)

The Virtual Console is emulation so they're clearly fine with it in principle, it's piracy of their games that they're not ok with whether it's in the form of bootleg games or ROMs.

The weirdest thing about Nintendo's stance on emulators is that their webpage assumes that you'll only be emulating things you've already pirated. They virtually don't even address the possibility that you're emulating games you legitimately purchased, except to say "well that's probably illegal too, or something!"