How to tell the difference between PSP 1000 and 2000 and 3000?

I'm curious about how one can distinguish between the PSP 1000, 2000, and 3000 models. Are there any visible differences in their design or specifications that make them easily identifiable? Additionally, are there any performance differences that set them apart, or do they all offer similar gaming experiences? As a gamer interested in purchasing a PSP, I'd like to make an informed decision and ensure I'm getting the best model for my needs. Could you provide some insights on how to differentiate between these three versions?