PSP Slim models 2001 to 2004F are the best.
1-Because they are smaller and lighter than PSP-1000. Also have 64MB of memory.
2-Battery last longer than PSP-1000 and even than PSP-3000. It has USB charging too.
3-These models support Pandora battery (thus can be unbricked easily and play homebrews).
4-The screen is brighter than PSP-1000 (not
as bright as PSP-3000), but doesn't have scan lines like the PSP-3000.
PSP-1000 best features are: IR port, doesn't feel cheap plastic, all models support and can create Pandora batteries.
PSP-3000 best features are: bright screen and internal microphone.
So PSP-200x > PSP-1000 > PSP-3000.