Now I'm wondering which is the chicken and which is the egg. Will trying to improve my foot position when I walk help my pelvic tilt, or will I need fix the pelvic position to improve my femur rotation and gait?
You've opened a can of worms here! Anyway, i'm just going to go wild with this one.
Of all the different resources that I look at, the general recommendation is to work on things 'from the ground up'. However, when we're talking about your every day postural issues, and assuming that I was forced to give a straight answer, then I feel that focusing on the hips first would be best. The reason I think that is because I feel that the imbalances start at the hips. I think this because the problem, or root 'cause' is sitting down too much and, well - you sit on your hips. So I feel it sets you up for the imbalances or should i say, the compensation patterns to follow.
In saying that, I don't even agree with myself. Often, we take our postures from our parents. Like 2 friends I have, both brothers, both had torn ACL's, and interestingly, their dad had the same injury. They look similar, stand the same way, and walk the same way - obviously nothing new there since kids mimic their parents. However, they are all quite knock kneed which will obviously increase the 'Q angle' which puts their ACL more at risk - same reason woman are more at risk, really.
When you consider that, which I guess would fall under genetics - then who knows where you should start!
You also need to address the specific imbalances. Some people have internally rotated femurs and so they compensate by externally rotating the feet. When you think of that case, then it would be pointless to try and fix the lower leg imbalance without addressing the upper leg / hip. When thinking of it in this context, then looking at the other scenario - externally rotated femur and feet (which I had) - then it looks like the foot is just going with the flow of the hip, and so you should address the hip first.
Gait is an interesting subject. Something I've not read much on specifically, but recommendations I've seen when referring to post rehab of a knee injury is to work on getting back to normal gait (i'm sure you know that often people continue to limp even after symptoms have gone) and the recommendation has always been to 'squeeze the glutes as your heel strikes the ground' - which again would imply 'prioritise the hips'.
In everything thats randomly coming to my mind, hips seem to winning on points.
Then you have the practical application. With externally rotated feet, then typically you have tight calves and ankles, with weak dorsiflexors. If you do soft tissue work, it only takes a few minutes to work over the calfs and plantar fascia. Moblising the ankle and calf is about one minute, too. On top of that - train the dorsiflexors, which is a quick exercise that can be slipped in anywhere in a program, really.
With the hips - well, if you do soft tissue work, you can go round your hole lower body in about 10 minutes. Whether this is done pre warm up or outwith the session is negligible, I believe. Stretching or mibilising whats tight can be added to the warm up, or betweem exercises that it won't negatively effect, and training the posterior chain should be priority anyway...
So maybe it's irrelevant what came first and we should be focusing on everything?
Then I think of my own personal experience. I used what I call the 'blanket approach'. I was the postural equivelant of the fat kid in denial the day he realised he was actually very fat. Furiously determined to fix it, I threw everything I could think of at it. From changing the way I sleep to setting a timer every 30 mins in work to remind me to stand up and /or fidget (reach for the sky etc). From doing a soft tissue work on my 'plantar fascia' to training my 'anterior neck flexors' (chin tucks!). So i've always felt that there's probably a lot of things that I done that you probably don't need to correct someones posture. But the more real life experience I get, the more I think that the blanket approach is the only realistic way of doing it. Certainly if your posture is REALLY bad, anyway. Truthfully, i'm not sure it could really be done without a big focus on soft tissue work, AND activation, AND mobility AND stability AND strength. I do believe that all of this can be implemented into a 45-60 minute lifting session, though (well, assumung you foam roll on the side). After that, all you need is the lifestyle changes (like fixing gait).
So, my preferred answer now that i've thought out loud via my keyboard about it, would be, "both".
You also have the same question with regards to the upper and lower body. Excessive kyphosis is often compensation for excessive lordosis which is a result of imbalances in the hips (and so on!!). Are you fighting a losing battle trying to fix kyphosis if you're not addressing lordosis? I actually think that you probably are. Perhaps the 'ground up' recommendations I have seen really mean "start with the lower body".
When I was at Cressey seminar in England about 18 months ago, he asked who had abad shoulder to get looked at. About 60-70% of hands went up. He assessed the guy right there infront of everyone - first thing he did was look at his feet.