Yeah normally for this sort of question we have a price, pictures of the device for quality checks and the like. For reference working ones on ebay seem to hover between $140 on the lower end (few scratches and the like) to around $200 for kept in a nice condition ones in terms of ones actually sold in recent times. That is a lot for a PSP from where I sit but I suppose it is now nice and retro, and somewhat rare.
Back in the day an unmodded PSP was basically deemed useless and the PSP go was useless even without that (no UMD, no easy battery, no hacks to match).
Today we have far nicer hacks and for some this does render the Go as one of the more desirable models over the alternatives. Usually because of the form factor than anything else.
In terms of pure "I want the best means to play this" (that is not a vita) then a nice 3000 or suitably blessed screen 2000 will be the kings of the castle (best screens, nice memory extras which some homebrew and ROM hacks do make use of and thus exclude the 1000). I can see the PSP Go being a serious contender or alternative though, certainly more than the Street and ignoring form factor or some inexplicable fandom for UMD it would take a very determined person to argue for the 1000 over a modded go.
The batteries are a pain to replace vs the regular PSP, and can suffer the same puffy problem of the regular PSPs.