Just riding along, in the moment, not looking at data after the ride, I monitor HR and cadence. I don't have a power meter. I pretty much ignore speed. If I'm following a route, I'll also look at distance.

HR, power, and cadence have a complicated relationship. Part of what makes it complicated is that it is affected by training and by the type of training one does. If one doesn't "train" but just rides along, then it doesn't matter what you do because you don't do anything consistently, so you won't get consistent results.

I'm of the opinion that HR is more valuable because it varies with hydration, temperature, and feeding, not less so. It measures physiologic stress, and that's a good thing to keep track of.

An interesting workout is to go out and spend a continuous 30 minutes riding at a steady HR while holding a steady 100 cadence through gently rolling hills. HR will have to be held high enough that you can climb, so in the breathing deeply and somewhat fast zone and of course you'll do a lot of shifting. As a result of this protocol, your leg effort will be constant.