Can you explain what you mean here? Keep in mind I have no experience nor familiarity with a PSP at this time, but a lot with emulation in general.
The PSP's screen resolution is 480 pixels wide by 272 pixels tall, which is 16:9 widescreen. Most systems up to and including the N64 (which you won't be able to emulate well on the PSP, so really most systems that you'd be able to emulate on it) primarily output no more than 320 pixels wide by 240 pixels tall. If you display the picture from an emulator at 1x, unstretched, it won't fill the screen — not even the top and bottom, as theres an extra 32 vertical pixels — so it'll be "windowboxed," which is a combination of both letterboxed (think viewing a widescreen movie on an old mostly-square TV), as well as column boxed (imagine the opposite, viewing an older TV show on a widescreen TV). In other words, you'll have black borders around the edges. And it really doesn't look
horrible, but it definitely doesn't look great, either. Not to mention old TV screens, which older consoles and their games are designed for, have pixels that are actually not square! They're slightly wider than tall, where each pixel is 1.125 times wider than it is tall. So the screen actually
should be stretched horizontally very slightly, but that means that (depending on the scaling algorithm) the likely result will be that the entire screen is rather blurry, as there's no possible way for more than one out of every 9 of the horizontal pixels to line up with the geometry of the screen. In other words, it won't look great.
Are there models or editions in the 3000 line that are recommended or should be avoided? Again, no familiarity with any PSP models at this point, but eBay shows a variety of those available.
The 3000 line is all pretty much the same. It's worth mentioning that the black ones show scratches and fingerprints very, very well, except for the Monster Hunter special edition version which is matte black instead of glossy. (I was tempted to get that model even having never played a Monster Hunter game, but being a limited edition color it was more than I wanted to spend on a PSP). The silver model actually is matte, although it's painted so it will still show scratches. The white model might be your best bet if you don't mind it looking like you're playing a PSWii, although I'm perfectly happy with the black model I have. Other than the colors there's no discernible difference between different PSP's in the 3000 series.
i would recomend to stay away from the E model (also known as psp street?)
only one speaker, no wifi (which nowdays is not a great problem, but wifi is still nice, specially for local multiplayer, i do think some emulators support it...
the psp 1000 is a heavy brick, 32MB of ram (all games are designed for 32MB anyway, the extra ram in latter models is only usefull for homebrew and to speed up loading times in UMD)
the good things about the 1000 is you get thumbs rest behind the L\R buttons, and it has a IR port, which can be used as a tv remove lol...
since the 2000 model they have 64 MB of ram (as explained above, doesn't really matter for games)
a AV out port you can use a cable to connect to TV and play on the screen, (primitive switch console anyone?)
the GO, has bluetooth which can be used to pair with a dual shock 3 (and i think a bluethoot headset as well? someone confirm this)
i barely tried a GO, but people say it's very uncomfortable specially with big hands
This also. Don't get the PSP E-1000. Another big issue with it is that the battery isn't user replaceable and it doesn't last very long brand new. Couple that with the fact that any PSP E-1000 you can find is going to be years old at this point and you can expect the battery life to be a joke that you can't fix (easily, anyway).
I don't think the original 1000 is really worth it, because the battery life isn't great and it weighs so much. Not to mention OP mentioned emulators, which means homebrew.
EDIT: another thing really worth mentioning is that the only SNES emulators for any PSP consoles rely on a number of hacks to run fast enough to be playable. This means they don't run well. Don't even try to play the SNES version of Yoshi's Island on a PSP without choosing between either graphical glitches, an unplayable framerate, or both.