I recommend going with GPS, but it will be hard to find a modern bike computer that understands power but not location. Having that data gives you more context, specifically how your efforts are impacted by hills.

Obviously you're going to need separate hardware (sensors) to measure your heart rate and your power, if you're to have that. You can use software to estimate your power use instead of measuring it, but most people consider that approach to be for entertainment purposes only.

Heart rate is cheap, power generally starts at about double what you consider very expensive for the computer part. Most people would agree that if you have a choice, a power meter and your phone is a better option than a fancy computer by itself - in terms of hitting the bike hard like you said.