Hello Kevin --
When fish die from something like a disease or parasites, it is important to understand that the disease was a symptom of a larger problem, inappropriate care. If you think about humans for example, the places where human mortality is highest is where humans don't have access to good food, clean water, etc. Disease usually sets in after the animal is stressed, and only rarely is disease the reason why the fish became stressed.
Pufferfish are not easy to keep. But neither are they impossible to keep. The most important factor is water quality. Like all fish they are sensitive to nitrites and ammonium, but they are also very sensitive to nitrates and oxygen levels. Broadly speaking, puffers need the largest tank you can use, with plenty of filtration, and frequent, regular water changes. The brackish water puffers appear to be especially sensitive, though this may be because salty water contains less oxygen than fresh water. Some people recommend 50% water changes, on a weekly basis.
If the only tank you have is a 10-gallon one, then a green spotted puffer is a bad choice, but there are dwarf puffers that might work out. To be honest, I don't really rate 10 gallon tanks as useful for anything except raising fry and keeping gobies.
It is extremely unlikely all the pufferfish in the shop have some mysterious disease that caused the death of the fish. It is possible, but unlikely. What is much more probable is that the fish have not been looked after properly, and are just generally stressed. If you bought another puffer, put it in a brackish (SG 1.010) water aquarium containing at least 30 gallons of water, and looked after it perfecty, I'm sure it would be fine. Farmed fish (like neons, dwarf gouramis, and angelfish) do very often come 'ready infected' with bacteria but by and large wild-caught fish do not. Feeder fish are, of course, one of the very best ways to introduce parasites and bacteria into an otherwise healthy fish since feeder fish are raised in overcrowded, unhealthy conditions.
The question you need to ask yourself is did you do anything wrong? Are there things you could do better? Have you access to information about these fish that you can rely on?
There is nothing wrong with admitting mistakes, and everyone loses fish from time to time. I did this weekend, having cut corners when trying to acclimate some new and rather delicate fish to a small aquarium, only to find them dead the next morning. So even after keeping fish for 20+ years, I still do silly things, and pay the price afterwards. Or rather, and more sadly, the fish pays the price with its life.
In your case, my guess would be that the tank wasn't mature, and that there was at least a low level of nitrites and ammonium, and these stressed the fish. The mucous from the gills can be a symptom of an irritation to the gills caused by the nitrite and ammonium. This is a short-term response fish have to protect the delicate gill tissues, but over the long term the mucous slows down oxygen getting into the fish and carbon dioxide getting out. The gills are also important as excretery organs, a bit like kidneys, and if they are irritated fish cannot "urinate" properly, which is obviously bad.
Two weeks isn't nearly long enough to mature an aquarium; six weeks is nearer the mark, and even then the bacteria population tends to be unstable. It is usually 2-3 months before an aquarium can be really considered stable and mature. One thing I hope you are aware of is that you cannot use zeolite (ammonia remover) in brackish water.
So should you keep fish again? Sure! It's a fun hobby. Should you keep a puffer again? Quite probably, but try and understand what mistakes you might have made and avoid them next time. As I say, these puffers are not impossible to keep alive (far from it in fact) and a mysterious, incurable disease is hardly likely. I would suggest using a larger tank, or choosing a dwarf species if you are stuck with the 10-gallon aquarium.
Sincerely,
Neale