Reverse voltage protection using a Power MOSFET at low voltages
You'll want a FET with low Rdson at the 2.7-3V Vgs so that you'll have minimal power losses when the battery is correctly inserted. The appnote you link to actually has some useful examples in table 1, e.g. it gives ILRML6401 as having 85 mΩ at 2.7V. That is worse than what the mfg datasheet of that FET promises (in the graphs below from the datasheet), but there's probably parts variation or the usual shenanigans where the mfg. measures with a brief pulse instead of continuous current. Note also that Rdson also depends on the drain current not just Vgs and the appnote didn't mention it. So you may need to estimate losses at say typical and max consumption of your circuit using different values for Rdson but only bother with that if there's substantial Rdson difference between these two use cases in the FET Rdson graphs.



You also need to consider the max (drain) current for the FET (make sure you don't exceed it) but for most coin cells it will be hard to exceed the current limit of SOT-23 package FETs anyway. Also, the current draw ultimately depends on your circuit. Power dissipation won't be much of an issue if you pick a Rdson under 0.1ohms; even at 1A drain current (which is tall order for most coin cells) that will mean 0.1W dissipation in the MOSFET.