Green spotted puffers are actually what got me into the saltwater hobby. I actually set up my 60gallon intending to get a GSP but ended up going with a Toby puffer for various reason. Because I was so interested in this puffer I did tons of research about the little guys. I actually responded to a few posts on this site about others who had some questions about GSPs.
I'm going to copy and past one of my responses, it does include a lot of answers/information about the housing of these guys, and some additional information as well.
"He would be fine in brackish for some time, and that is what is usually suggested when they're younger, then onto full marine conditions as adults. There is no harm in acclimating him to full marine to begin with even at his size/age. So you could definitely acclimate him straight to marine if you wanted to.
After my research, it seemed it would have been easier just to go to straight marine rather than brackish. Mainly because of cost and filtration options. Filtration options in full marine (addition of live rock, skimmer, etc.) vs brackish are more efficient. Once the saltwater tank was established (if proper filtration is utilized) it wouldn't require as many water changes as a brackish (especially true to high end brackish) tank. Obviously frequent water changes on a high end brackish tank would add up in cost with all of that salt. It just makes more sense, especially if you already have a saltwater tank (in your case) or would be going to full saltwater eventually anyway (as I was intending to).
If you wanted to set up a tank just for him, which would be great too of course, the size could depend on the salinity you would be housing him at. A 30g minimum is recommended for a single GSP but that size would be best for brackish. To attempt full marine conditions in a 30g to house a GSP full term would be problematic because of space. The live rock needed for ample filtration would take up a lot of that space/water volume. Thus making it difficult for a full grown GSP to swim and less water volume would pose problems with water quality, as I'm sure you know puffers are high bioload.
For full marine conditions, I'd say something like a 40g breeder (similar size/footprint) would be great for a single GSP."