I'd advise you to watch it first, then read after the anime has ended.
The anime is like...friggen awesome.
Word of advice though. Bleach has some pretty interesting fillers, but they interrupt at such awkward times in the main story line that it become infuriating. HOWEVER, what i would suggest is figuring out where the main arcs start and end, watch one arc, watch a filler arc, and then go back to the main one.
Course you could just watch everything related to the main arc and then watch the fillers, but you will most likely be less inclined to watch the fillers then.