What about PSP Go? Sure UMD's are dumb, and I'm sure it's not that important if you're using it as a emulation machine. But I can't imagine you'd want to pick that model unless you could get for a way lower price than other models.
I actually have a PSP Go! It's the only fully working PSP I have at the moment. If you really like the smaller size, you'll probably really like it, but otherwise, just stick to any other model. The buttons are sort of cramped and don't have much travel at all, so it's a little hard to play fast games like DJ Max and Mega Man on it. And it doesn't use Memory Stick Pro Duos like every other PSP, so you can't use those nifty MicroSD adapters:
But it does have 16gb of storage built in and takes Memory Stick M.2 cards, so that's not too bad. Higher capacity M.2 cards are very rare, though, so I've only got a 4GB one in mine.
Positives: PSP Go also supports Bluetooth for whatever reason, and it's the only model PSP that can, so you can use Bluetooth headphones if that's your thing. You can also sync it with a Dualshock 3, but through a fairly convoluted process by hooking it up to a PS3, for whatever reason. There's also a "pause game" function which is essentially a save state, but for full PSP games, so that's nice but you can only save one state at a time. The speakers are remarkably good and much better than the PSP-1000 ones, especially considering this is a small handheld from 2009. Also, mine's sparkly white, and while I don't normally like glossy white electronics, this one's different. Pictures just don't do it justice, so if you get the chance to look at one in person, check it out.
Negatives: The battery isn't easily removed, there are a few screws on the back but I'm not sure if it's sealed in like a smartphone or if you can just pop the back off. It also uses a proprietary charging cable that was only made for the PSP Go, unlike every other model of PSP that uses the same cable. It looks like a Vita cable, but isn't compatible at all. It also needs its power brick to charge from a dead battery, which is obnoxious because mine does that thing where if it sits in a drawer for a couple of weeks, it'll be completely dead since the battery life's not great. There are component cables for TV play, but they're not cross compatible with the normal PSP cables, so bear that in mind.
The PSP Go does feel very solid and the screen slides really well, so it's a pretty nice thing to hold, and I'd recommend it if you just want a small PSP. But if any of those drawbacks turn you off of it, then just stick with another PSP model. I like mine, but I only spent $50 on it, and I honestly just wanna repair my old one with a bad analog stick and use that. Normal PSPs have much bigger buttons and are more comfortable to hold.
Is there any reasons you shouldn't get it functionality wise? I know you can find other models used that are about the same price, and it has the form factor of a door stopper, so I'd agree it shouldn't be a first choice. But as far as I'm aware its functionally's the same as the other standard models minus the 3D, so I'd think it would be fine if you could find it for extremely cheap, and give zero fucks about 3D and horrifically ugly it is.
If you can get one extremely cheap and don't care about taking it anywhere, then go for it. But, it doesn't fold at all, it's one solid piece, and the screens are just as small as the original model 3DS. It's also from the "old" generation, so you can't play the smattering of "New" games on it like Xenoblade and Minecraft, and SNES9x will run slower.
The "New Nintendo 2DS XL" is more or less its successor, which
is a fully-featured New 3DS but without the 3D, and the D-pad seemed a little clickier. But it's at least a proper clamshell, which the 2DS isn't. The 2DS was released around the time Pokemon X and Y were coming out, as it was intended for kids who might be rough on it and snap the hinges on a clamshell 3DS, so unless that's a problem, every single other model is better. Buy a 2DS only if you can get it for absolute dirt-ass cheap.
