I use the Bound Sword. I forget if it requires a perk to trap souls.
A black soul gem is much easier to fill yourself than a grand (or even a greater) soul gem, as those two require the soul of a major creature, but a black soul gem will take the soul of any humanoid, and they're everywhere...
EDIT: One more thought about soul gems, although it doesn't really apply to your black soul gem issue... If you fill a soul into a larger soul gem (say, a lesser soul into a grand soul gem) all you have to do is drop it and that will empty the soul in it. Putting it directly into storage (a chest or whatever) does not seem to lose the souls bound within, so that's safe. But haphazardly collecting souls does not permanently junk up your soul gems.