The PRV you show has unions, not pipe threaded joints. Those do NOT need tape or dope. The union nut brings two flat ends together onto a gasket, normally. The seal is NOT made by the threads.
Pipe threads for water need a sealant - teflon tape (properly applied) or pipe dope (a semi-liquid or paste type product) are the options there. Teflon tape is slightly harder for a novice to get right, and the cost of a small tube of dope and a roll of tape are not dissimilar. So I'd suggest dope.
If you choose tape, it must be stretched as you roll it on in the same direction the threads run, and it must not be over the end of the pipe, where shreds can break off and clog valve orifices downstream.