You've heard right. Everything you mention can be part of improving your overall fitness, plus more if you want to talk longevity. To get longevity I focus on body systems - so what/how do I work out to keep each of my body's main systems strong? Longevity doesn't happen if you have a weak heart, poor circulation, or weak breathing capacity, nor if you are frail and lack strength and balance. Address each system's unique needs to stay fit and encourage longevity.
There are a lot of choices of exercise to work on each area. You need to decide for yourself, perhaps hire a personal trainer now and again, who can analyze your current body condition and make recommendations for exact gym routines to do, number of reps, etc., and keep track of your stats. Then add non-gym sports and fitness to get yourself outdoors and in nature.
My advice is try many things, find what you like, and make them part of your (daily or whatever) routine. For me, it's cycling, walking, hiking/climbing which > is cardiopulmonary, circulatory, some muscle groups; plus gym > upper strength and core, plus add'l endurance cardio on machines to fill in outdoor downtime. It's pretty neat what can be accomplished in a few years of dedicated effort, you only need keep at whatever you like.
One additional benefit of regular, specific exercise is that when something isn't behaving right, you'll recognize it straight away.
Edited by Oakman, 02 October 2017 - 11:53 PM.