read the POH.
do not pump the throttle, as the aircraft is fitted with a primer, use that if you need to prime, which you shouldnt need to if it's only been shut down for 15 mins.
Pumping the throttle puts an unmeasured amount of fuel right next to the cylinder, the amount will vary depending on how hard/fast you pump the throttle, which seriously increases the chances of an engine fire.
They wouldn't fit a primer if they wanted you to prime it using the throttle.
The throttle does need to be set more open than a cold start for a PA-28.