Sensitivity is crucial to feel the more subtle bites and weight is important because you will be holding the rod up in the 9 to 10 o'clock positions for long periods of time. Graphite rods are lighter, more sensitive and faster than most fiberglass rods. You want a fast rod with a medium backbone to get a good, fast, hookset. It is important to have a soft enough tip to maintain tension on the fish at all times. Many times, when you hook a fish, only the point of the hook will be embedded and unless you apply enough tension, you can get slack in the line and easily loose the fish when it gets close to the boat.
Weight is vital when holding the rod up for extended periods of time.
Flipping rods are designed for removing fish from heavy cover in shallow water. Pitching and flipping go together. Look at the tip, make sure it has some flexibility. This flexibility will make it easier for the angler to make quiet entries into the water and makes pitching much simpler when necessary. Your flipping stick should be made of lightweight graphite and have a stiff backbone to pull those fish out of heavy cover.