I'm wondering which model is better to own if you're not a fan and just want to play some third-party games from all systems (GB, GBC, etc.) with most accurate sound and video? Maybe emulators on PSP will do the right job? I heard what PSP emulator of GBA is even better than the console itself because of the backlit.
If you want to run everything, get a GBA. If you want it to be backlit, get a GBA SP. If you want a better looking backlit screen, get the AGS-101 GBA SP or the GB Micro (the GB Micro is not backwards compatible, though). However, it's my view that original GB games are best played on an original GB or a GB Pocket because all the later models attempt to "colorize" GB games, and they tend to look pretty awful. There's also the GB Light, which is basically a backlit GB Pocket. That's probably the best you can do for original GB games, but obviously it's not compatible with GBC or GBA games.
But there are various button combinations for different colours that you can access during startup. One of them is pure greyscale. I use that when playing original GB games on my AGS-101, which happens to be the best solution for playing GB, GBC and GBA games.
PSP is a cheap emulator, so I guess that's your best option. Of course you'd need a memory card.. Be sure to buy a second battery, GBA Emulator drains so much battery it's laughable.
Yeah, this is what you should do (though Yoshi and Metroid II have pretty good auto-pallets). There's even a green-tinted greyscale option if you prefer the classic look compared to the nicer true greyscale.