Training data, what works?

A power meter won't let you perform beyond your maximum heart rate. A heart rate monitor plus power meter go together well. I use a heart rate monitor and am well happy with it.

Trainer Road is a front runner in training plans. It requires power, cadence and HR.

You do an FTP test at first, the software then has a number to base all your workouts from. They have thousands of workouts, but also the best bit, multi week plans which gradually increase in intensity/duration to enhance your FTP. 4 to 6 weeks into a plan you're re tested and you should have improved 3-5% if you're already fit. Much bigger gains if you're starting from a lower level of fitness

What do you want to achieve? Do you want to be coached or use tools like Training Peaks?

If you don't then something like a power meter is a luxury and could even be counterproductive. Information can be useful but numbers can turn every ride into a target-chasing exercise. Even a cadence sensor can be a distraction if you're not using it for a specific purpose.

But if you've got some money to burn then a multifunction Garmin-type thing would dent your bank account effectively. Whether it's genuinely useful for you is another thing entirely.

You can go to the nth degree with any of the sports you've mentioned, cylcing is no different.

For training, I'd say a HR monitor is probably the cheapest most useful thing you need. 

If you buy a cycling computer, most will come with cadence and speed sensors.. 

HR, Cadence, Speed. That's what most people will use.

If you're okay flashing the cash then a PM will also help you monitor and measure yourself, best when used alongside the other sensors and not on it's own... of course then you'll need a training app as well to tell you what to do and where you're at.. Training Peaks is good for that... 

It all adds up... most people I ride with are happy enough with a HR monitor and strava.