I feel compelled to rephrase the initial posting in a microeconomics way:
"Which of these items can be done that consume fewer resources than the resources that are recovered?"
People sometimes forget that true treasure hunting is actually salvage. About making choices that maximize personal EV (expected value). Salvage is about spending less money to recover the item than the item is worth. In the case of coinshooters, the vast majority fail this acid test. Their time, gas, lodging, and ammoritized equipment cost, etc, don't add up to a positive return on their resources. But they have a large 'pleasure' return to their component so they do it.
Treasure hunting as a pro, is definitely going to need a positive return on resources (time and money). So it becomes a resource economics problem. This can not be ignored. That leads questions to be asked. What activity brings a positive EV with lowest risk? What activity brings the highest positive EV with medium risk?
#5 Gold prospecting overseas immediately popped out as a high favorite. Especially in developing countries where locals will not have grubstakes to buy the right equipment. However, the prospector realizes he is a target for robbery and needs to factor that cost into his equation.
#3 Cache hunting has the greatest appeal to most as it can be done part time at first. Low cost, and negligible tax burden depending on ones conscience. Whether it can be done profitably depends upon the statistical size of the caches recovered. The rate of recovery will depend on 3 big factors:
1. Research quality and quantity (lead viability)
2. Social engineering (charm factor) to get on target land
3. Speed which #1,2 are done.
Therein lies some interesting variables for cache hunting. Those in hilly country may specialize in moonshine caches, those in mafia territory may go after ill gotten stashes, those in cross border drug traffic areas may go after smuggling caches, while those in old farmland areas my go for post hole banks. I believe certain specialty niches will have cache types statistically too small to sustain a pro. I suspect the best caches to go pro on would be life savings caches.
But to reflect on the overall essence of his post. The correct answer will vary by person and circumstance. I have the luxury of having built a business, have staff, and can travel on expeditions for weeks at a time without risking a steady income. Given this situation, #3 is my correct answer. However, other occupations, with different time demands, family pressures, political problems will have a different correct answer. Like perhaps #1 (shipwreck recovery) for a seasonal fisherman who already owns a boat and Scuba gear. Or #2 (Hard Rock Mining) for a plumber who lives in Arizona near gold country.