I'd certainly start the least expensive way.....and it will probably cure the problem. Yup, shut off the water, pull the stems & take them with you to the hardware store.
IF you end up getting complete new fixtures, in my opinion, stay away from Price pfister & Moen. Go with American Standard or Symmons. Price Pfister actaully isn't bad, but they change styles every 5 minutes & parts can be hard to find next week. Moen is popular too, used a lot in motels because they last about forever, but, they also suck about forever. They work great when brand new, but within a year they are either full on, or full off, it's their nature.