by utilizing the accelerator pump you can prime the engine for starting and this is often the preferred way.
I disagree. If the airplane has a hand primer, it should be used rather than the accelerator pump. The reason being that the hand primer will atomize the fuel to a much finer mist, being drawn in with the air better, greatly aiding combustion, and reducing draining back as a liquid. That's why they're hard to push, you're pumping the fuel through a tiny orifice to atomize it, instead of shooting a stream into the carburettor throat. And, the primer nozzle is further downstream in the inductions system, reducing draining back. Drained back fuel is a source for a carb fire. Pumping the throttle does help a stumbling engine at start, but is not preferable over a primer. The Cessna and Piper POH's do say to use the primer....