At the moment I'd say Saints play the most interesting and adventurous style and have frequently been there or there abouts. Harlequins also play exciting rugby but seem to have a lot more variability in their performances. Case in point, a few years back they lost all their games and were bottom of the table, they then sacked their coach and won everything, including the league iirc.
Bath have a strong history but have only really found reasonable form again in the last 3 years or so.
Saracens used to dominate everything but their style was a bit divisive. They still retain their style but have not had quite the same degree of success.
Tigers have a reputation for being very traditionally English, forwards dominated and also have always been there or there abouts.
I suggest watch a few games and gear in mind the form can fluctuate quite a lot. See who gets you excited and just go for them.