There are many styles of playing shakuhachi, and no single style is necessarily "the most correct." What I'm outlining here is what I've taken from my own experience after learning from many teachers of many different styles, as well as from reading articles by various teachers, both older and contemporary, on their playing and breathing styles. If possible, I would suggest that you do the same - learn from a variety of teachers, go ahead and learn forms, and notice what you like and what you don't like. No one can tell you how to play, just like no one can tell you how to live your life. This is your style, and it's your decision. Your job is just to find out what you like. This is what I like, and is probably the playing style that is best suited to my shakuhachi.
Kennech Dychtwald has an excellent book, Body Mind, that outlines how various mental postures affect our physical postures, and vice versa. Imagine a proud, muscular person who walks about with a puffed-out chest, unafraid of the world. Now imagine a more sickly person, who always seems to lack the energy to engage the world. He walks around hunched over, head down. The first one is open in his heart area, but the second is protecting himself. This was me until I realized that a gluten intolerance was crippling my energy levels. I was hunched over as if I was guarding what little energy I had left, trying not to let in any more stimulation.
Your physical and mental postures affect one another. If you can't manage a particular posture, it is possible that, like me, your problem comes from somewhere else. Maybe you need mental or physical healing before you can sit up straight. Don't force it. Be kind to yourself. If you can do so without straining, though, this is how I recommend you hold your body.
Sit up straight, chin slightly tucked in, keeping your neck from craning outward. You want to make a straight path for your breath to travel up through your abdomen, chest, neck, and out through your mouth into the shakuhachi. Let it feel like a string is pulling the crown of your head up toward the sky, and let your torso and legs feel grounded.
The key word here is "open." Tuck in your pelvis a little to open up your abdominal area. Let tension drain out of your chest down your back so that the chest/heart area is open. Hold your arms out, lifting them without putting undue tension into your shoulders or elbows, as in standing meditation practice. If you can sit seiza (tucking your legs under and letting your buttocks rest atop your feet), it will give you more breathing power, but sitting on a chair or standing are also acceptable.
Again, hold the flute "out." Most people have a tendency, especially at first, to hold the flute almost vertically. This is a very closed, restrictive position, and it will make it difficult to play and breathe smoothly. It's best if you can hold the flute out at at least a 45-degree angle, or even more if you like. Make a habit of noticing when you start to sink in your posture, and open yourself up again. An open body will encourage a mental posture that is more open and present, able to accept new things and people.
Your lips don't need to do anything in particular, but this may prove difficult to put into practice at first. The ideal is to keep your lips relaxed, with just enough tension (and no more) to allow a tiny stream of breath to leak out when you increase your internal air pressure. You don't want to go so far as to make an "o" shape with your lips, nor do you want to pull them to the side. I have known several teachers with roots in the Tozan school who teach that you should pull your upper lip taught to adjust your aperture, but myoan (fuke / Komuso) players that I know, as well as Yokoyama-school players, generally keep their lips as relaxed as possible.
If you want some things to experiment with, here are some other tips. I know of one master who would play with a small "air bubble", or pocket of air between his upper lip and his teeth, letting his lips almost puff out a little bit and allowing air to leak out of the embochure between his lips. Another Myoan player I know specializes in "fat" shakuhachi with large-diameter openings (24mm+) at the top. In order to adapt to these, he inserts his tongue between his lower lip and lower teeth, puffing out the skin below the lip to cover the hole. This takes some getting used to, but it's a good method for playing fat shakuhachi.
I know that lots of teachers to lots of work on embochure, but my teachers never said a word about it. If you want to do intentional work on it, that's good, but if you find it distracting, I think it's fine just to forget about it. Just check in a mirror to see that your air is moving toward the mouthpiece, and then leave it alone. The more you learn to relax, the more it will develop - and like many things (and people!), they grow the best when we're not putting pressure on them to "grow!"
For those that need a good starting spot, however - an aquaintance of mine, Erik the flutemaker (google him - he lives in Florida), says that you should "spit watermelon seeds." This is a great image of what it looks like. You are not making an "o" with your mouth; you are simply closing your lips and then letting up on the pressure until there's room for a little bit - a watermelon seed - of air to leak out.
There's a sutra that suggests that you take a short in-breath of 3 seconds, pause for 2 seconds, and breathe out slowly for 25 seconds when you meditate. Modern science has confirmed that a short in-breath and a long out-breath help to relax the body and calm the mind. For Christians as well, this makes perfect sense. Look at Gregorian Chant (as well as modern hymns and praise music) - when you sing, you take in a short breath and then expand your out-breath for 10 - 20 seconds or more quite naturally. This helps us to focus on the words we're singing as well as the God we're singing to. This principle has changed my life since I started chanting the psalms with the old Gregorian psalm tones rather than merely reading them.
Your breath should be a full-bodied breath, using all of your breathing spaces (rather than just the chest or just the abdomen), but with the emphasis on the hara, or the abdomen. My studies and experience have led me to a place where I keep my belly out on the in-breath, and push it out on the out-breath as well. It has the effect of helping you to breathe deeply and relax your diaphragm. Many Myoan players teach the same thing. Again, Akikazu Nakamura has written entire books on the subject - he, too, plays with the abdomen "always out." One guess as to how this developed is that when you wear a Japanese Kimono, the belt (obi) supports your abdomen in a way that makes keeping it "always out" is quite natural. These techniques often happen simply by accident, but it's no accident that players have held on to this aspect. As long as it's not uncomfortable, give it a try for a while. For me, this is the best way to breathe when playing shakuhachi.
Don't worry about your mind.