Hi there, I'm not a "puffer Whizz" But do know a bit about them as I keep them myself. My situation was similar to yours, my kids wanted them so we got them, irresponsibly knowing very little about them but we got them through and they're looking fab so hopefully we can get yours through too
Right, the very very first thing you need to do is get that salt out the water!!! Yes GSP's are salties but indroducing salt to their water needs to be done gradually not all at once as it can shock them and kill them. I would suspect that the LFS had them in straight tap water, please try and check this as it's important. If they were in tap water start raising the salinity by 0.002 once a week. Get a brackish low end hydrometer check your tap water S.G. and add enough salt to take it up by 0.002. (Add the salt, which needs to be marine salt to the bucket of water as adding it directly to the tank will burn the fish inside and out) (Also a black bucket is better as you can see whther the salt has fully disolved or not)
The next thing is to get the tank cycling. GSP's as you say are not the best but, I made the same mistake as you and managed to cycle my tank with the Figure of 8's insitu (loads of experts tutting!!!!) You need to get a test kit as a priorty, the paper test strips are rubbish so try to get a liquid one so you can see what the ammonia nitrIte and NitrAte are doing. Be really careful on the ammonia and nitrite stage as these are the killers. If the only way to cycle this tank is with GSP's in place you'll need to test your water daily and be prepared to water change frequently. Please go and get some PRIME it's a water conditioner and will help with high ammonia and nitrate levels. Also go back to the LFS where the fish came from and ask them for an old filter sponge from their fresh water system as this will hold the beneficial bacteria and will help jump start the tank by putting it in your filter. The old bacteria that was in your tank would have suffered big time from the sudden salinity increase. At the same time pick up a load of plants as these will also help with the cycling.
While cycling you need to be keeping the ammonia as low as possible by keeping up with water changes as every time you water change you are diluting the ammonia level, and the same with nitrites and nitrate part of the cycle. You can use stuff called ammolock but in my opinion I don't like the stuff as it only works for 24 hours, affects the building up of the beneficial bacteria and shows up on your test kit as an untrue reading, other people may scream at me for this but I much prefer to keep water changing to combat it.
The website thepufferforum.com is fabulous and there's loads of info on what they eat, tank set up etc online, but in the meantime, get yourself aquainted with the nitrogen cycle (if you don't already know about it, sorry assumed you don't to be on safe side) and keep a very close eye on the water parametrers, it'll be hard work but you can do it, I did and we're all through the other side safely (took about 3 weeks)
This will get you going, I'm off to Disney today and not back til Saturday but will try to check back in a couple of days to see how its going. Leave me any Q's and I'll answer for you. Good luck.