Will we ALWAYS NEED a handy man as a career field?

Yes, there should always be a need for handymen. But, handymen are typically self employed meaning no company benefits such as health insurance, a retirement plan, paid vacations, etc. Of your other choices, construction, electrician, plumber, and carpenter are tied to the new construction industry and at times, like now, there is very little work to be found. Personally, I still like electrician because it is clean work without a lot of heavy back straining type work. And, even during slow construction times like now, an enterprising electrician can find remodel and repair work if he or she works at it. Another growing and reliable field is refrigeration repair, and HVAC, (heating, ventilating and cooling). You are smart to be thinking ahead while many of your peers cannot think past the fun they might have today or tomorrow. Young people with a plan are twice as likely to be successful than those without one.