Melee hunting is the fastest and has a bonus of increasing Strength which in turn increases carry capacity. Powerfists might be slightly faster than other weapons (due to higher weight of Melee Combat skill) but the difference is probably negligible.
In the long run, whatever activity has the best bottom line financially will be the best for your HP as you'll be able to recycle the same PED more times. Level ~35 in Prospector/Surveyor will give you approx. +10 HP from Prospecting/Surveying/Mining/Drilling, and while it takes time, you might well make profit along the way.