It's an interesting question but you must be prepared for the answer that there isn't one.
That being said, I have been taught several "fundamental sets".
The nine this, the eight this, four of this, four of that, five of this, six of that. the eight plus three, etc.
These sets seem to suggest that the eight basic moves are practiced first in wuji stance and then later with stepping.
Thus there is no fundamental stance other than to maintain central equilibrium in and out of (during) the 'stance'. Using single whip is the biggest endorsement of 'settling' you will find in Taijiquan, and the first place it is taught, if anywhere else. And why! If you read between the lines, like in the story of liu musan. Secondly (another way to look at it) is the idea within taiji separate to xingyi etc. is that wuji is for health and taiji/taiyi is for martial. Meaning, that the end position of single leg stances is the yin yang transition, which makes sense given taiji theory.
Thus for all intents and purposes you will need to practice wuji stance and the eight gates in wuji, then forward/backward stance, then with various stepping. Since this then becomes the form you will look at the eight fundamental movements in wuji as the "mother palms", with wuji itself being the supermother (father?) "palm". Now, what you really want is a posture which holds your arms up. But you also want one which is consistant with a common tai chi move. So single whip is a good one. There are reasons why single whip in particular is chosen for standing, one major reason is that it is basically the first
application taught in push hands that comes from a form move. That is why it always appears after grasp bird's tail.
So basically, start with wuji, then practice the basic elements of grasp bird's tail, then practice grasp bird's tail, then progress to the corner moves starting with single whip. Beyond that, I have been taught special standing exercises for raise hands, and a few others, but who has the time for all this stuff these days
p.s. with extremely few exceptions (lou xi ao bu etc) if you use a posture not found in the first quarter of the form your probably doing it wrong. I will let the cat out of the bag this once, if you are hugging trees you are not doing tai chi, that isn't a tai chi posture. Teaching is another matter but as for "mother palms" in the sense that all CMA are based around the same fundamental structure of design elements, that isn't a design element found in tai chi is it (for example). So then why! do people do it
Because they're
desperate don't know any better.