-Sith, at their core, are fairly volatile and savage creatures, given to impulsive acts of violence, with a deeply-rooted need to dominate others. These traits have been passed down from before they became a hybrid species, and tend to be hidden behind a more civilised outer veneer inherited from the humans who conquered and bred with them. That inner psyche will be more or less pronounced in some individuals, to the point where many Sith exhibit their 'outer' traits more strongly. This juxtaposition - the combination of barbaric Sith heritage and more civilised Human influence - is probably the most important point, and a lot of a given individual's personality will stem from where they fall along that scale. Vilesha for example fell very much on the human end of the spectrum, being a very focused and controlled individual who subconsciously tempered her species' worst excesses with complex philosophies (her attitude towards slaves being one of noblesse oblige rather than viewing them as disposable chattel, for example). But even then, during combat she would become increasingly driven and aggressive as her more primal aspects came to the fore, and she remained prone to bursts of extreme cruelty and violence when particularly stressed or confronted with someone who had personally slighted her.

-Rampant egotism is another common trait, and explains the Sith's tendency towards infighting and betrayals. Many Sith view themselves as the centre of the universe, the protagonists of their own stories, and naturally assume they know better than everyone else. They believe that if everyone would obey (or be forced to obey) them, and them alone, the Galaxy would naturally fall into its right and proper order. An extension of this is that I visualise most Sith as not favouring destruction for destruction's sake - they want to build and create, but that necessarily involves tearing down other, 'lesser' works and societies to make room for their own quite obviously superior creations. You can see something of this in the colossal tombs and statues which litter Korriban, as testament to the species' desire to build great things and be remembered for all time. They remain proud and arrogant, even in situations where they have no reason to be.

-Another aspect which has been passed down is a natural inclination towards hierarchies. The original Sith species was split into genetically distinct castes, and while individuals could increase their standing within that caste, a Massassi (warrior) could never ascend to become a Kissai (priest) or vice-versa. While those castes no longer exist as distinct sub-species, the mindset remains. If an individual demonstrates their strength, individuals who view themselves as 'weaker' will naturally fall into line, at least until such a time as they believe themselves to have grown stronger. Interesting this isn't restricted to Purebloods - the original Sith species very quickly bowed down and accepted the Jedi Exiles as their rulers once they demonstrated their superior might and technology. The Sith's casual acceptance of slavery also stems from this - to them it's perfectly natural for weaker individuals to labour for the betterment of their superiors, and many probably struggle to understand precisely *why* Republic-influenced species find it so abhorrent.

-Oaths, honour, justice and vengeance are all culturally important, though they might be expressed in unusual ways - Vilesha wouldn't see anything dishonourable about shooting a fleeing enemy in the back (they remain her enemy, and might rally to trouble her in the future) but wouldn't countenance any action against an opponent who surrenders themselves into her custody (as they're now her slaves, and as the stronger party, she is obliged to protect them just as they are obliged to bow to her will). I pulled a lot of inspiration from the ancient Aztecs, samurai-era Japan and hard-line Islam, with weird combinations of bloodthirsty aggression, rigorous discipline and a strong focus on personal and family prestige.

-One upside of the Sith's more primal nature is they are all very passionate, hot-blooded creatures. They don't just love; they obsess. They don't just get angry; they hate. Everything is driven to extremes, leading to wild, often over-the-top reactions when they aren't deliberately trying to control themselves or channel that energy into something positive. Their art and stories would probably be wild and epic things, full of self-destructive lovers, mighty heroes driven beyond their means, and other such acts of poetic excess that exalt their inner fury. Leading on from that, I imagine that most Sith struggle to feel a lot of long-term accomplishment in anything. That fury leaves them impatient and unwilling to rest on their laurels, driving them to better themselves (and others) over and over, until eventually they over-reach. Their lives are short but spectacular.