My kids have started taking swim lessons at the Y, so i've been sneaking up stairs to run a mile during their lesson. I've thought about strength training etc, but I have no idea what i'm doing on those machines.
Can't say I feel any different, but it is enjoyable.
Pretty much anything that makes your muscles feel sore and doesn't cause injury is worth doing.
IMO: most of what makes fit people fit is becoming aware of their body in detail: how to use muscles, how they work, what they feel like, what they should feel like when they're working together -- all of this builds a foundation where, if they lost their fitness, they would just get it back again.
So if you don't know what you're doing: just learn by doing. Pick something that it seems like your body should be able to do easily, but can't, and fix it. Repeat x100 and you'll be fit as hell.
You can start with bodyweight though. Pushups, pull-ups, etc. I recommend the YouTube channel FitnessFAQs or Calisthenicmovement for a good start there. No nonsense, direct guides with discussion of technique and injury avoidance.
I find the rowing machine is a great cardio+strength combo that you can make as comfortable as you like, and is very low impact (just keep good posture).
Running is a good start. Keep the distance increases reasonable to avoid injury. Enjoying it is important - no need to add anything else until/unless the running gets boring. (Yeah, weights can help, but like you said, can be overwhelming for somebody new to fitness)
It's not perfect, but it was great for getting into the habit 3 times a week. Now I often make up my own sets as I go, taking note of what's sore on me and what I feel could use some work. Doing that gave me the time to do research and get a bit more familiar with how to engage certain muscles, and what machines will do what for me.
> I have no idea what i'm doing on those machines.
Book some regular sessions with a personal trainer. He/she will give you a balanced basic routine and teach you good form.
I was fortunate to have an excellent PT when I first ventured into the gym age 19, a skinny, awkward, scared teenager. The structure of that gym program is still the basis of what I do 30 years later. Different exercises get incorporated, depending on my goals at the time, and variations in # of reps and sets. But still the same general approach.
Strength training is so good for desk jobbers! I recommend joining some small group circuit training or CrossFit groups, where the trainers will show you how to lift correctly and safely.
Just try some pushups, dips, pull ups, and sit ups. Just do a set of a few types each day until your strength is depleted and you will see strength gains.
Can't say I feel any different, but it is enjoyable.