You can get one of those air filters that sit in an office on a desk, and turn that thing on before you start dealing with your ash, and leave it on for a while after. It'll make a difference, believe me. Our TV is above and to the right of our fireplace, and I always stick the chop vac hose up on it so it can draw dust out of the TV.
Also, about vaccuuming out the ash:
Wood ash is quite fine, and will plug up your shop vac's notmal filter in short order. I do use the vac, but only when I'm doing a deep cleaning inside the fire chamber. Cleaning ash from your 25.00 shop vac filtr is damn dirty and tedious. I make pre-filters out of various materials I come across, and rubber band them over the normal filter. Even with that the standard filter gets clogged, and I use the compressed air to blow it out. After about 10 times, it's pretty well embedded though, and I get a new one