I currently have 7 briars (with another one on the way), one meerschaum, and plenty of cobs (cheap and easy, not too hard to throw away and replace). At max I smoke 2-3 bowls a day for any given week. I try to dedicate 2 briars to aros, 2 for Va/Per & VA, and the other 3 to English blends. The aro and VA pipes end up getting mixed some of the time but I do try to keep the Latakia pipes separate. Beyond that there's really no method to my madness, I try to smoke every pipe before I start the lineup over again. Sometimes I'll smoke 2-3 bowls in a row out of the same pipe but not usually more than that before letting it rest and moving on to the next. If I've already smoked all of the pipes dedicated to one blend and they haven't had much time to rest I'll smoke the Meer or a cob to give them more time. I also turn to the Meerschaum on the odd day that I have the time and plan on smoking 5+ bowls. I plan on expanding my pipe rotation over time, not necessarily out of need but because I enjoy collecting them.
To the point of your question though, if you smoke one bowl a day I'd say 2-3 pipes. If you smoke multiple bowls a day then you might consider at least 7 pipes, one for every day.
Happy puffing!