"Does it mean that the right shall not be infringed *solely* because of the need for a well regulated militia? Or because that need is just one good reason?"

It means that in 1789, there was no confusion. If the country needed to be defended, all male citizens who had weapons WERE the de facto militia! They had an odd assortment of weapons, and it was presumed that when not defending the country, they used them for hunting and VERY occasionally, self-defense or settling scores..(dueling did exist).
When writing the 2nd amendment, they had no idea we'd have either the social problems, or the weapons technology we do today.
'Interpreting' what they meant now is done by deciding what you'd LIKE it to mean, then constructing an argument to fit. What is needed is a revision based on current issues....... fat chance! (Bobert explained it quite well)