Guppy I follow my checklist and guess what it says pump the throttle
Perhaps you might be a little more specific as to the aircraft, checklist source, type of carburetion (surely you're not pumping the throttle in an injected engine), and if you have an updraft carburetor.
I've seen a lot of poorly written checklists that have incorrect information, or lack in presentation.
Do you understand what the accelerator pump is, how it works, and it's limitations?
Am I not understanding your penultimate paragraph? I hand-start my little Continental A-65. Are you saying that, following priming using the pump, I should not suck in?
If penultimate means the last paragraph, then it specifically referred to use of the accelerator pump. If you're referring to the second to last paragraph, I did discuss pulling the engine through after priming. Some feel this is an appropriate cold weather soloution, though it does remove lubrication on cylinder walls, increases the possibility of a stack or intake fire, and in the case of hand propping, can dramatically increase the impulse and RPM rise when the engine does fire.
If you're hand propping an airplane that has no other way to start, then yes, you may need to prime. You may, like some, prefer to start on the prime, then advance throttle. I always advocate caution in doing so, and discourage people who flood out the engine and then pull it into or through the engine by moving the prop. Depending on your priming system, you may not be pulling much in.