Average speed and time are really dependent on the external conditions whereas measuring power is not affected by external conditions.

It may help to think about power in terms of on bike performance. To go faster you need some combination of pushing harder on the pedals or turning the pedals more frequently, which can be measured with power, which is how much energy you put out per unit time. If you training is going effectively then you will be producing more power so it is an effective tool for determining whether or not your training is working or if you need to change things up. BTW this is a very basic description of training with power and does not take into account the many nuances of doing so.

I use Cateye Strada (NOT the wireless version) https://www.cateye.com/en/product_detail/279
Does all you want except with a wire and there is a wireless version.
If you run a front brake, then the wire is basically hidden.
Can mount it on stem nicely as I do with it.
There are many other similar options to the Strada, some cost less even.

I also use sometimes the Garmin Forerunner. But I mount it on the handlebar when I use it (with a rubber spacer) - wouldn't think of having it on wrist. For most rides the Garmin and the Cateye match to within .05 miles.

Al

It's a good thing having your computer on your handlebars, best place to look at it. They easily unclip from their mounting bracket so you can take it with you. I bought my wife the Micro wireless and it's great.

As for heartrate, get yourself a separate heartrate monitor that is on a wristband. You can then use that when running or at the gym. They aren't very expensive.

You might check out the Training and Nutrition forum. There is a lot of information you may find useful.

Thanks for that power description jonestr. I can dig that. Like, I might be hauling ass one day with a tailwind but putting out less power than the next day going slower in a headwind. I'll check the training forum too. I looked in the gadgets forum but it was mostly about lights, and I wanted to know what people in here have used.