Do you think that that could apply to Class 3 firearms?
Probably not. While it doesn't specifically say that reasonable restriction is allowed, it keeps the status quo in place, though is worded much better for us. Common use is easy to prove and argue, reasonable restrictions is entirely opinion. In order to have it apply to class three you would have to prove that such weapons are in A) Common usage and B)That the registry, $200 tax stamp, and wait are a defacto ban. If anything I would say it might be possible to use the ruling to overturn state prohibition on class three items. But making it as easy to buy class 3 as any other weapon is very unlikely. But, using it as an individual right, you could have more ground to argue against it.
Also how common does it have to be to be considered common?
This is what is so much better for us then if the opinion had allowed reasonable restriction. Common usage can be proven and argued fairly easily. Handguns (auto and wheel guns), rifles, shotguns, "assault rifles", etc. are all in common usage. Under the common use clause we have ground to fight on, reasonable restriction would have had us fighting much harder with more chance of using because it would be solely up to opinion.