People talk about the Big 5 or Big 6 or Big 7 strength exercises because they are the most time-efficient. They are time-efficient because, as a package, they can stress and gently damage pretty much all of the useful skeletal muscles. Controlled muscle damage is the goal. These are large compound movements which should leave you breathless, fully-fatigued, and aching if not hurting a bit.
If you can do them, you don't really need to do any other strength exercises. All you do is increase the reps up to near ten, and/or the weight. For middle-age and older, we think 4-5 sets of 10 or fewer reps while steadily increasing the max weight, and each exercise once-weekly is enough unless you are a competitive athlete. I mostly do 5 sets with the first being a warm-up weight and the final being my max of 6-8 reps if I can do it. (Over ten reps is always a bad idea unless for small muscles (eg calf, forearm, isolated triceps, leg machines.)
I consider the Big Seven strength exercises for guys and gals of any age to be the following:
1. Squats (with body weight, goblet, ideally barbell, or whatever you are able to do. I now do back barbell squats to sitting low. Sheesh, what a bitch that is.)
2. Pull-ups (for guys mainly, but assisted works for gals or for guys who can't do them. Or gals can substitute pull-downs on the machine - much better than nothing)
3. Deadlift (+/- snatch, etc)
4. Bench press
5. Military Press
6. Barbell or Dumbell Rows - hating them means you need them
7. Dips
Not one of these requires a gym machine. Gym machines can be of use to get yourself to a level where you can perform the Big 5 or 6 or 7. Gym machines are also excellent for warm-ups (eg pull-downs, leg extensions, leg press, press downs, etc). That's mainly what I use them for, but most active people have developed some joint problems over time so the machines can be less-good substitutes for the Big Ones as needed. (I have one wrecked shoulder, but lots of people in my gym have a wrecked knee or two or some sort of back injury, fake knees or hips - or something. A bunch of cripples!).
These are just strength exercises, of course, for muscle-preservation and improvement as the clock ticks but they stress the heck out of your heart too, which is supposed to be good. Some cardio and some calisthenics need to be part of a balanced program with also, ideally, a sport or two for fun, social fun, and as the reward.
Feeling over the hill is a mental problem. We had a guy here who was still lifting 3 days before he croaked at 95. Dead, but dead in pretty good shape for his age. Can't ask for more than that.
