The Chaldean order is the order in which Man descended through the spheres and was granted his powers of demiurgy by the governors in the Divine Pymander. We can trace hermetic planetary ascent rituals to the Abassid Caliphate being practiced by the magicians there. Hermes Trismegistus instructs us in the Divine Pymander to move up through them making specific sacrifices of attachments in order to deify ourselves. This is echoed a lot in alchemical literature as the alchemists reference frequently that if you do the operation out of order you will need to restart the work.
Now you can definitely initiate into the spheres in any order you want, but you will not be granted the same transformation. In the Golden Tractate of Hermes Trismegistus the vulture cries out that he is the black and the white in the black and the white and the yellow in the white and so on and so forth. This is particularly clear instruction on why the order of operations is so incredibly important when making "the crow fly without wings", that is, the souls transcendence through the sequence of operations. The vulture is stating that within every stage the beginning of the next stage is seeded.
So you can, for example, initiate into Jupiter and then Venus and then the Moon and reap immediate magical effects, however, you will not be performing the ascent ritual which can take up to a decade, and in this, the Opus does not happen. So if you just want magic dont worry about the ordering, if you want deification then do the spheres in the right order (Moon -> Saturn) because all of the Hermetic discourses are very clear about how to approach the governors to become as Poimandres.
