The above discussion applies only to the muscles mentioned (chest, back, shoulder, various leg muscles) and ignores "The Core." People define the core differently, but it usually consists of the abdominal, obliques (a kind of abdominal) which are together often referred to as "The abs" as in "hey, dude, my abs are ripped"; the lower back (which we pretend to be one big muscle) and perhaps your hip flexors. Maybe your hip flexors are in the "lower body - pull" category. Your choice.
Core is important. Just like rotator cuffs (which are technically part of the core as well), the core supports other body parts and muscle systems. And, the core is often under-worked and not well conceptualized by the average gym-goer.
For instance, lower back spasms (in the muscles ... not talking about spinal injuries here) are probably often caused by weak abs. When the abs are weak, certain movements may stress the lower back. Sure, a lower back spasm may be caused by a weak lower back, but if you only work the lower back to avoid future spasms, that will not be enough. You need all of your core body muscles to be in shape to avoid injury.
Ideally, you will work the core a lot when you start a stint of exercising (as in "I think I'll start going to the gym", not "I'm going to the gym today like I do every day" starting). Once your core is up to snuff, you should work it almost every time you go to the gym, and you should work the core last. You don't want your core exhausted when you need it to support your central body while doing heavy lifting. Let the core help you through your routine then work it at the end, abs first, lower back last.
The only other significant advice I have regarding the ordering of your efforts is this: If you want results with a particular muscle group, work that set of muscles when you are not tired. Go to the gym earlier in the day, do those muscles, if you can, earlier in your routine, and if they are muscles you normally do last, then make that all you do that day.
Resting: Resting is important. If you hit your muscles hard every day with a well designed routine but no days off, for a few weeks, you will find that if you take two days off and go back to the gym, you may be able to lift more weight with more reps than the last day before your rest. Rest is part of muscle building. How long to wait between working a muscle (at the large scale, as in what muscles to work on what days) varies with the muscles, the person, and your level of training. Here's some basic principles:
Larger muscles need more time to rest.
If you work out more often, you might be able to reduce rest time from two days to one for large muscles.
Some muscles don't need rest. You might be able to work your abs every day, for instance.
You can tell if your muscles are 'rested' because that post-workout pain you get the next day is done with.
You can shorten required rest time by proper stretching after working out. I'm not talking about stretching in this discussion because I have nothing useful to say about it, but you are supposed to do it whenever you exercise AFTER you've worked out. Not before. After.
Well, OK, I'll say something about stretching. But first another issue: Before you start pumping iron on a given day, warm up. Spend ten minutes at moderate level aerobic exercise to get your heart rate a little bit up, your joints loosened up, etc. Do NOT stretch before working out. Then, after each intense set of exercises on a given muscle group, do some properly done stretches on that muscle group.
Resting is even more important than you suggest. Exercise per se doesn't increase strength or endurance. What exercise does is activate the compensatory pathways that during rest restore the muscle function plus a little more. The degree of activation of those pathways determines how much âgainâ you have. Pain triggers gain, but there are other things that are more effective (nitric oxide for example).
So, Greg, how do you plan on enticing your scibling Ed to the gym? Hee, hee.