The target colour space will depend on the source material you are playing.
If playing SDR videos, Rec709, with a 2.4 EOTF/Gamma.
If playing HDR, then Rec202, with a PQ EOTF, using multiplier to deal with the difference in peak luma.
There are no 'consumer sources' that are P3.
(Some LUT Boxes/HTPC systems will map from the Rec2020 HDR source down to P3 pre-displaying the image...)
Steve