Czerny, who was Beethoven's student and wrote many books for increasing one's piano technique (his exercises are still regarded by many as the gold standard), give a precise description of good posture for pianists on pages 8 and 9 of LETTERS TO A YOUNG LADY ON THE ART OF PLAYING THE PIANOFORTE. The book is available online free and also through Amazon, which publishes a nice reprint.
Basically, though, here the bottom line on posture at the piano, from Beethoven through Czerny straight to you:
"acquire a graceful. . . position, when sitting at the pianoforte. The seat which you use must be just so high, that the elbows, when hanging down freely, may be a very little less elevated than the upper surface of the keys; and if your feet should not reach the ground. . . have a dwarf stool. . . made of a proper height, to place them upon. You must always seat yourself exactly facing the middle of the keyboard, and at such a distance from it, that the tips of the elbows may be a little nearer to the keys than the shoulders. Equally important is a graceful position and carriage of the head and upper part of the chest; it must neither be still nor bent. . . .[don't make} a cat's back. . . sitting with their backs bent and oblique. . . . It is not merely that an awkward position is disagreeable. . . but it also impedes, if not prevents, the development of a free and elegant style of playing. The forearm of the arm (from the elbows to the fingers), should form a perfectly straight, horizontal line; for the hand must neither rise upward like a ball, nor be bent so as to slope downwards. The fingers are to be so bent, that the tips of them, together with that of the thumb, when extended outward, may form one right line; and so that they keys may always be struck with the soft and fleshy tips of the fingers, and that neither the nails nor the flat surface of the fingers shall touch the keys. In striking the black keys, the fingers must be stretched out a little more; but even in this case they must always remain sufficiently bent."
My own experience (not Czerny) is that the advice about the tangerine in the hands is good advice.