Though my somewhat-intensive studies on the matter (in my own scattered-yet-immersive style), I've found a very close correlation between the sephira spheres on the Kabalistic Tree of Life and the planetary spheres of classical Hermeticism. I actually find sticking to the planetary names and attributes to be more clear and helpful than using the former system.
Here is a diagram of how each of the planets fit into this system in hierarchical order:

A quick disclaimer is in order before proceeding further: The Plolemaic system is meant to be a metaphysical cosmological map, not a literal map of our actual physical solar system. Anyone witha 3rd grade science education knows that the Earth is certainly not the center of the solar system. In other words, the map above is heuristic device used to explain metaphysical principles; it's not the territory itself. We moderns have this knee-jerk impulse to grossly empiricize everything under the sun, to to speak. The ancients didn't really think like this. I've actually run into a few people (in this case, Rene Guenon fanboys) who believe
literally in this geocentric model as being our physical reality. They are missing the point of it entirely and are spiritually and mentally consumed by their lower ego and thus have little interest in exploring the mysteries beyond the most superficial level with an open mind and humble heart.
Having gotten all of that out of the way, we can now move into the map itself. In this system, each of the 7 sacred "planets" function as receptors and transmitters of primordial cosmic energies or intelligences (i.e "the gods"), according to the classic Hermetic sciences. There are both higher and lower aspects to the planets, with the lower aspects manifesting when the different planetary energies intersect here on Earth in an inauspicious manner. The highest aspects are the benevolent qualities each planet represents. The hierarchy starts with Earth, but the Earth isn't a planet itself in this scheme, but rather the starting point on our enlightenment journey. The basic outline, in order:
Moon (Luna/Selene/Diana): Raw intuition and creativity, also the reception of all the other planetary energies and the transmission of them down to Earth. Associated with the Water element. Luna is the first step on the enlightenment path; it's the initial "wake-up call." The lower nature of the Lunar sphere consists of things like neuroticism, mental incontinence and even insanity, hence the word "Lunatic." The person who fails to pass the Lunar sphere is the person dominated by their unconscious mind; they run most of the time on autopilot and have difficulty exerting agency over their own affairs. In the world of art, Luna is the raw creativity. It's the Solar power (Apollo) which gives art its useful and inspiring form.
Mercury (Hermes/Thoth): Messenger of the gods and associated with the Air element. More specifically, this sphere represents the communicative and flexible powers of nature. Mercury is the power of intellect and thus the ability to understand higher wisdom/teachings within a coherent intellectual framework. Passing this sphere requires the ability to think clearly and rationally. However, remaining stuck in Mercury means the initiate cannot surpass the act of merely intellectualizing higher wisdom; without the ability to master the next sphere (Venus), the initiate will still be driven by emotional impulses, passions and desires. The "master debater" sophist, the legalistic pharisee and the arrogant professor are all potent archetypes for this type of Mercurial arrested development. The lower/malign aspect of Mercury manifests in the various misuses of the intellect that bring much harm and misfortune to others. Tricksters, con-artists and clever liars in general, are all archetypal associations of the dark side of Mercury.
Venus (Aurora/Aphrodite): Goddess of love and bonding. Venus represents the passions and the emotional side of human nature. Lower aspects are our lusts and animalistic appetites of an emotional nature. Passing this sphere requires the ability of the initiate to master his or her own emotions. Failing to pass the Venus sphere means we are still slaves to our emotions. Esoterically, the Venus sphere is the principle of attraction. It's associated with the element of Fire, but this fire is "flowing" and persistent, as opposed to the arid fire of Mars, which simply consumes things and ceases when that consumption process is complete. Venusian fire lingers until its actively dissipated or the burning energy moves onto someone or something else. Think of Venus as heat in a humid medium, say an environment like a tropical beach. Whereas, Mars is a desert environment.
Sun (Sol/Apollo): Represents the heroic and healing role the initiate will embody on his or her path. The Sun is the giver of life and energy. It represents vitalistic activity and energetic manifestation in general. A saintly person or a true altruist is the type of person who has mastered the Solar sphere. The Solar hero is truly a "son of God" if we're to understand what that means beyond all the trite platitudes which have been associated with that symbolism over the past many centuries. Solar Savior figures are clear representations of the Sun archetype when applied to the actions of sentient beings. The Sun is also a symbolization of Celestial Fire in an apparent form that humans can make sense of.
Mars (Pyroeis/Ares): Mars is the god of war, in the most superficial sense. However, on a more primal and esoteric level, the Martial sphere represents the harsh and unyielding Judgement aspect of the enlightenment path that must be mastered before ultimately breaking free of one's earthly fetters; it's raw willpower. Whereas Jupiter is the benevolent Sage or Hierophant capable of practicing genuine Mercy, Mars is the series of trials and tribulations that must be passed before the hero can truly become an enlightened master. Really, there's no Mercy without Judgement. Martial activities and endeavors are quite self-explanatory. Mars is a fundamentally male energy and thus its essence is supremely cut-and-dry and lacking in nuance. Whereas Venus, the mundane female energy, is a tangled web of ebbs and flows, meandering curvatures, and convoluted nuances.
Jupiter (Zeus/Jove): This sphere has been subject to a whole host of misunderstandings largely due to the fact that various sky gods also functioning as pantheon heads have been associated with this sphere without much in the way of finer explanations being offered. To clear up this confusion we should defer to the Indian understanding of what Jupiter represents. The Hindu shorthand term for this sphere is "Guru." The benevolent and wise teacher (or Hierophant) is the true essence of this sphere. The mundane aspect of Jupiter is fortune and prosperity; think of the word "Jovial" as an example. Combine this with its kabalistic association with Mercy, which can only really be attained once Judgement is mastered. Plato's concept of the Philosopher-King may perhaps be the best characterization of the aggregate sum of what this sphere has to offer.
Saturn (Kronos/Rhea): This oft-maligned planet represents the constrictive and limiting aspects of nature. It's associated with the Earth element and thus the Saturn symbolism of things like blockages, obstructions, austerity, restrictions, conservatism, stodginess, caution, rigidity, old age, slowness, stubbornness, the act of thwarting or stymieing, ect., easily comes to mind. If Mars is the sword in battle, then Saturn is the shield. If Mars is the accelerator on a car, then Saturn is the brakes. In essence, the Saturn energy is the final gatekeeper of this manifested universe of limitations, sorrow, troubles, death, ignorance, disaster, destruction, ect. We could perhaps say that Saturn is the Ouroboros (the serpent who eats its own tail) or the Wheel of Fate/Samsara. Saturn is the final tests before a soul can truly gain immortality of consciousness and escape the cycle of death and rebirth. At this stage, the initiate will have transcended all of their worldly desires and thus have balanced out all of their karmic debts. The highest aspect of the Saturn sphere is the Great Mother Goddess, which is the primordial energy that gives form and solidity to everything in manifested existence. Many of the Neolithic and Bronze Age serpent cults understood this symbolism quite intuitively.
The functions on this chart higher than Saturn constitute a whole different topic for another time.