You should run your pump/filter as long as it takes to keep the pool clean. Some pools have great circulation combined with low use, therefore run times can be quite short. Other pools have lousy circ systems and huge bather loads and even 24/7 filtration has trouble keeping up. Don't worry, most good pool equipment is made for 24/7 use. When I quote a new motor I sometimes get informed about the much cheaper motors down the road. Remember a Pool Pump runs 24/7 under full load. A bench grinder motor runs a few minutes occasionally and half that time is spent free wheeling, not the same at all.
Chemistry is a major part. Get a good test kit that does Free Chlorine, Total Chlorine, pH, Total Alkalinity, Calcium Hardness and Cyanuric Acid (Stabilizer). Use it every day until you understand whats going on. Believe me, it will pay off. You might use a ton of test reagents but in 2-3 weeks you should be testing way less. You will probably find you test calcium once or twice a month, alkalinity once or twice a week, stabilizer once a month but chlorine and pH are pretty much ongoing. Depends a lot on your system, your use and your fill water.