How long should I run my pool pump for?
In general the point is to filter your water.  If you want to be sure about it, check the volume of your pool, and the flow rate of your pump.  Run it long enough to go through that much volume 1-2 times a day.  In practice, that's probably around 6-8 hours.

Make sure your chemistry is good, and then try it.  If it looks nice for a few weeks, try lowering your operating time and see what happens.

As a side note, 1.5 HP is 1120W.  That's probably peak power not normal consumption, but you should still assume it consumes somewhere around $0.10/hr or so.