strong/ weak conductor

That's pretty much it. Salts of the group 1 elements will always dissociate completely, which is what makes a strong conductor in solution. However, if you had, say, vinegar, which is an organic acid, most of the molecules would stay together and only a small fraction would dissociate into the H+ and CH3COO- ions. That makes it a weak conductor. You can't always tell just by the formula if something will be a strong or weak electrolyte. You just have to know.