This could be an entire day at a personal training conference, so forgive me if we generalize a fair amount.
General warm-up
You want to go with dynamic over static stretching. Static is a more relaxing type of stretching. We don't want to do that to our body before getting into more intense exercise. We want to gradually up the intensity, which dynamic stretching can provide.
Having said that, I've had some clients who whether they be into yoga, in their 50s and used to habit, they're going to do static stretching before they start their weights. I've had clients get to the gym an hour before me to do this work.
Which brings us to weights being part of the warm-up. If someone does whatever type of stretching before we start squatting, it's not like we just jump to their max squat weight. We still warm-up that exercise, which in effect is adding more dynamic stretching.
That is, the static stretching isn't some huge no-no / the person is going to die. It's not desirable, but it can be worked with.
Specific warm-up
If you're someone with a shoulder surgery history, you might have some exercises you want to do most won't care about. Like some rotator cuff work.
Weights vs Cardio
There are no hard rules here. Prioritization is the theme
If you're someone who is interested in maximizing their running
performance, then cardiovascular work should typically be done first.
If you're most concerned about lifting performance, then lifting
should be done first.
You do what's most important to you first, because that's when you
are freshest. Whatever is done first, gets the most attention, as
attention is a finite resource.
You used the compound lift vs isolation lift example. That's mostly true. Mainly because compound lifts are more intense, thus riskier -a bench press is riskier to your shoulders than lateral raises- so they should be done when a person is least fatigued.
However, if you're a bodybuilder looking to build up your triceps and bench pressing isn't hitting them well, you might not care about compound movements being done first.
- For most, they don't have a dominant goal. In those cases, you do
whatever works best for your schedule. The biggest concern with
everyday people is actually sticking to a routine.
For my personal training clients, if they have to see me at 5pm due to work, I'm not going to tell them to take off work early so they can do cardio first. We'll train first, which will be mostly resistance training based, then they can hit the cardio afterwards. Or, we'll simply make the resistance training have a cardio element too e.g. circuit training.
If a more intense cardio like running wants to be done, then maybe we'll lighten up the leg work beforehand. And that doesn't necessarily have to be every day. If we train three days per week, but they only run two, then we still have one day we can hit the legs harder weight wise.
I've had many clients who will train in the morning, then walk at night, because doing both is too much at once time wise. That's perfectly fine. An alternative would be telling that person they need to wake up earlier. That's miserable for most, and misery isn't a longterm accomplice we want.
Warming-up within weights
Let's break it up by upper and lower body.
If it's our first upper and lower body lifts of the day, we want to warm-up. For average strength, I work people up to their work sets with 2-3 warm-up sets. (More strength, often more warm-up sets.)
If we're in the latter parts of the workout, then the warm-up can be cut down, if not taken away. This is exercise dependent. If after doing some bench pressing, you then go to rope tricep extensions, you probably don't need much of a warm-up for that exercise.
If you're going from bench pressing to chin-ups later on, then you want to warm-up as you did for bench pressing. Chin-ups are a much more intense exercise (use more muscle mass), and the muscles involved are not related to bench pressing. Bench pressing gets the triceps warmed up; it doesn't get the biceps.
Flexibility / Mobility
I go with filler sets. Example:
In the first two exercises we work the pecs and lats (amongst other muscles). In the third mobility exercise, we loosen up those muscles.
I typically either go this route of work an area, then loosen that area, or I break it up by body section. Where we work the upper body, then loosen up the lower body.
In another part of the workout or another day, we'd work the lower body but loosen up the upper body.
Most people's time between sets is either sitting down, looking at their phone, or walking around. Doing some mobility work is more productive, and not likely to take away from the lifts. We can also add some more work for that bum shoulder.
(Because we're in the middle of the workout here, this is still primarily dynamic type mobility / flexibility work.)
Core work is towards the end
It's commonly thrown out that 80% of people will experience lower back pain at some stage.
The core can be part of this. But it's not usually core strength which is lacking. It is typically more a person's ability to use their core for long durations of time, or while fatigued.
For instance, have someone do a plank, and it's going to be easier for their core to hold their back in neutral at the beginning of the workout than at the end. In this case, we actually want to feed into that fatigue.
Translating that during the day, if a person has trouble with anterior pelvic tilt, they can typically hold themselves in neutral if they think about it. The tough part though is being able to do that for hours at a time.
(This is just one example. Low back pain is rarely this simple.)
Cool down doesn't have to be cardio based
People's most favorite time of yoga is the end. They often lay down on their back, work on breathing, and listen to some Enya.
I like to do a version of this. I use these two exercises:
Hip Rocking: https://www.youtube.com/watch?v=DSSGeymXUgw
Belly Breathing w/Arms Up: https://www.youtube.com/watch?v=2BP9GA5VvWs
The theme of the cool down is relaxation. Think of it like a movie. If a movie is good 90% through, but the ending sucks, that influences disproportionately how one feels about the entire movie. Endings matter.
By making the end of the workout as relaxed as we can, we can change how one feels about what preceded it. More details in Making your (memory of your) workout more enjoyable.
Getting on a treadmill in a gym, where it's typically loud, busy if not zoo like, isn't the best. Hey, if you workout at home and can do a cool down by yourself on your treadmill, or out in your backyard with trees, then alright. But I usually put people in a corner or the aerobics room where it's quietest and have them stretch the thing most commonly tight- the low back, and work on some deep breaths into the stomach.
Summing up
The bolded above are a solid order:
- General warm-up with predominantly dynamic stretching.
- Specific warm-up based on how your body is currently doing.
- Weights or cardio, with a warm-up specific to that exercise e.g. if you're going to start running, you don't start running at your maximum pace.
Lessening of warm-up later on in workout. If after doing chin-ups you're going to do bicep curls, you don't need the same warming-up, if any, that chin-ups necessitated.
More flexibility / mobility within the workout to increase productivity of rest sets.
Core work
- Cool down, relaxation focused.