Resistance Training: Let's Keep it Simple
Lift heavy things. Get stronger. Does it really have to be more complicated than that? Well, perhaps not and it really wasn't for most of human history. But few of us find ourselves in professions where we're constantly moving, carrying things, digging, hammering stuff, et cetera. We're now in a world where we like our data to count, steps matter, and strength gains are measure in plates, not hay bales. So for those of us who rely on a gym to take the place of natural obstacles, how do we know we're getting the most out of our workout?
If you're new to the gym, the great news is that it won't take much to see improvement. I would encourage you to set a small goal: show up three days a week. That's it. Walk in the door of your fitness club and your job's done. But how does that build muscle, I hear you ask. It builds something more important: a habit. If you can lay the ground work of simply going to your gym or park or wherever you do your workouts, you'll find your excuses will begin to fall away. Just showing up may only take 10 minutes out of your day and you can begin to find more creative ways to make and use that time. Then, success begets success. One small win, just showing up, will lead to another: I moved more weight today than I did the day before. This is the process-oriented mindset that can take you from where you are now to any (realistic and achievable) goal you set.
So you've got the going to the gym habit set in motion. What's next? Should you stick with 3 x 10 on the cable pull down machine? Pick a random weight off the rack and knock out some curls? Discretely copy what you see other people doing? Well, if your objective is to prevent muscle loss with age, the good news is, you don't need anything complicated, you just need, well, anything! Anything 2-3 times a week at just 20 minute doses each time. If you do have goals beyond preventing muscle loss and you want to see overall strength gains, it's much more preferable to incorporate more compound and "functional" movements into your routine and consider bringing a coach or experienced friend on board if you're after something more specific.
What do we mean my "compound" and "functional"? I think those are terms that are thrown around a lot without many specifics. They way I would define them is any movement that replicates a pattern you might use in every day living. Mind you, I'm more referring to living the way our ancestors did, not so much our modern ways. So, picking something up from ground level to chest or above head height or pulling your own body weight up from the floor to head height would be to great examples. You're moving in free space and operating within your body's range of motion to either move an object in space (as opposed to along a fixed axis) or just move your own body wight in that space. Then what are some ways we can replicate these movements in the gym, at a park or even in our homes without making it complicated? Here are some suggestions...
Focus on free weights. I'm not just taking dumbbells. This could be medballs, kettlebells, or anything that's "free" and not attached to a fixed plane of motion. This includes your own body weight I'm not necessarily saying that the gym machines don't have a place, but you'll almost certainly be acting on a much broader muscle group with "free" weight lifting. Consider a squat. The weight is either your own body or whatever you have in your hands. You're going to recruit upwards of 200 independent muscles all acting in unison to perform the movement while keeping your balance and your center of mass stable while being acted on by an external force. Contrast that to a basic leg extension machine: no coordination required, your midsection stabilizing muscles can go to sleep, and at no point throughout your daily life will you extend the knee joint in isolation.
A note on sets and reps:
As far as the number of repetitions, again, it depends on your goal, but if you're just looking to incorporate a little more movement in your day by using a gym facility or a dedicated space in your home, your reps and weights should depend on when you start to fatigue. If you're doing push ups, for example, each set should last until close to muscle failure, then rest and repeat. If you just did one push up at a time and paused for a while in between, you would miss out on adaptations that would only occur with acute build up of metabolic stress that only happen as a result of repeated reps at a lower rate. If you're lifting close to your maximum weight, it may only take 1 to 5 reps before you get a sufficient amount of positive stress to incur adaptations. Basically each set should be close to failure but you should leave the workout feeling energized and stronger than when you came in, not fully fatigued from doing set after set after set in the name of better health.
Target your legs first. If we're going to the gym with out a specific plan, I notice the tendency is to focus more on "vanity" exercises to hit the CORE and the BICEPS to look good naked. There are a number of flaws with this approach that I won't get into here, but the bottom line is that working on your leg strength first is going to set you up for better success when working on the rest of you. A result of activating those 200 plus muscles in a squat is a greater release of adaptive hormones in the blood stream. If you follow up your core (this is not just abs!) and arm work with leg work, you'll see greater potential strength gains than if you did core and arm work by themselves. 
See the park through the same eyes as the kids. I can almost guarantee you there is something available in the park for you to jump up on, swing from, or pull up on. Why relegate quality time with the kids at the park to the bench? Join them! Hang on a bar, play tag, anything that keeps that movement momentum up throughout the day. Not quite ready for pull ups yet? Simply hanging from a bar or sturdy tree branch can help improve grip strength, stretch your lats, and decompress your vertebra after, just what the doctor ordered after a long day sitting.