It depends on the purpose of the P-wave phase picking. In the case of the event location there are multiple approaches (the first extreme value, the first evidence in amplitude above background noise - AmpSNR, the first evidence in frequency above background noise - FreqSNR). The optimal picking strategy may depend also on the used travel-time calculation algorithm (ray tracing, eikonal equation, etc.). I would also recommend to check particle motion to avoid mis-picking of an another phase. One has to be also cereful, not to pick artificial P-wave precursors caused by acausal anti-alias filtering. In the case of the focal mechanism determination, you should pick a band around the first extreme value to retrieve the first-motion polarity. The most important rule is to be consistent in picking among multiple stations and events. See also this document: DOI: 10.2312/GFZ.NMSOP-2_IS_11.4