Wikipedia should tell you what's the difference exactly between all 3 PSPs and the PSP Go.
You shouldn't convince yourself to get a PSP 1000. It has 32MB RAM, compared to the 64MB RAM that all other PSPs have. Everything loads faster, SRB2PSP runs better, etc.
And eventually, you'll want to plug the PSP on your TV. With the PSP 1000 model, you can't. There's a way to do it, but you have to buy this huge device for the PSP that makes it bulky, so it's not worth the trouble.
If you're not planning on hacking the PSP, then get the 3000. As Mystic said, you're better off buying used games than buying brand new ones online for the PSP Go. The Go screen is smaller, anyway.
I have the phat PSP 1000 model, and I never heard of any advantages it has over the other two PSPs. Other than it's the easiest to hack, of course. Eventually, I'll sell it and get myself the 3000 model.