Appearance:
Spock is a somewhat imposing figure, standing at about 6’2” and having been described as having a “demonic” appearance. His upturned eyebrows and pointed ears lend to this imagery. He also has glossy black hair that’s been shaped into a bowl-cut, as well as dark eyes that can appear very serene or burn with an incredible intensity, depending on the circumstances. He has pale skin that can appear greenish due to the color of his blood, particularly if he becomes flushed.
Personality:
On the surface, everything about Spock appears stereotypically Vulcan: cool, calm and collected - professional to the extreme in many ways, and he takes great care in projecting as much. This is seen by his formal speaking patterns, his efforts to remain composed during a crisis, how he takes care not to demonstrate anything that could be considered favoritism towards those who are close to him, and even the way he occasionally straightens his uniform when he stands.
He was raised on Vulcan, where the teachings of Surak maintain that logic should dictate all thought and actions, and that emotions should be tightly repressed. This came about because, as Spock’s father Sarek states, emotions run deeply and strongly within Vulcans, and, in many ways, are even more powerful than that of Humans’. Without logic to keep them in check, Vulcans are prone to becoming dangerously violent, and Spock is well aware of this.
As purely Vulcan as Spock tries to appear, however, in actuality, he is quite conflicted. Spock is half Vulcan and half Human -- two halves that he has a difficult time reconciling with one another. To say Spock is completely motivated by logic would be somewhat untrue; indeed, it’s most likely a very emotional need for acceptance among his Vulcan peers and his Vulcan father that drives him to hide his emotions under an icy mask of logic. And yet, being half Human, there is another side of him - perhaps the side that allowed himself to kiss Uhura publically before beaming aboard the Narada - that occasionally surfaces. However, sometimes these breaches in his façade can have dangerous consequences, such as when he nearly strangled Kirk on the bridge. Spock likely understands that becoming emotional is not only a hindrance to his duty, but also a detriment to the people he cares about (his TOS counterpart said as much once), and so this probably serves as another reason he tries to suppress his feelings. It would explain why he seems to stay clammed up even when he’s alone with Uhura.
Perhaps his duality is partly why he cultivated so many options for himself as he became older. Obtaining kolinahr, and purging all emotion, as well as accepting his admission into the Vulcan Academy of Sciences, would have been among the highest achievements a Vulcan could have aimed for, and yet Spock ultimately turned away from those things and chose a career with Starfleet. Vulcans typically don’t join the military - such a move went against everything a traditional Vulcan was expected to do, and Spock was well aware of this. The council for the Academy of Sciences accused him of trying to satisfy his Human half’s need for rebellion, when he was likely satisfying his need to find a place where both sides of himself could be tolerated, perhaps even embraced. (In TOS, Amanda states that Starfleet is the only home Spock has, which seems to lend credibility to this idea.)
That’s not to say Spock shuns traditional aspects of Vulcan culture, though. As mentioned earlier, he’s very serious about following the ways of Surak. This is obvious not only in how much importance he places on relying on logic, but also by the traditional Vulcan dietary practices he follows, such as not eating meat and never touching food with his hands.
Also, despite being a military officer, Spock only resorts to brawling when he’s angered and can’t think straight. Otherwise, he considers it a very uncultured and undignified way to handle a dispute, which is an attitude common among Vulcans. He’s much more likely to deal with an enemy using a swift neck pinch. Simply put, Spock has no taste for bloodshed when he’s in his right mind, which can be considered an odd trait for someone who’s essentially a soldier. Needless to say, it’s the satisfaction of scientific research that makes serving onboard a starship relevant to his interests. He respects all life forms, and generally dislikes taking life if he believes there are other alternatives. However, this isn’t always the case, particularly in instances of a more personal nature, as seen by the way he questions Kirk’s offer to show mercy to Nero. We also see him reverse his “no-killing” attitude in TOS when Kirk is in danger, so his movie incarnation would probably behave similarly if people he cared about were being threatened.
His relationship with Amanda Grayson, his mother, is an important facet of Spock’s duality. While Spock often endured harsh criticism and bullying from his peers growing up, his mother often assured him that, no matter what path he chose, she would always be proud of him. In this sense, Amanda may have been the only person in Spock’s life who truly accepted him regardless of which half he chose to identify with. She meant a great deal to him, and seems to be a large factor in the motivations behind his choices. The way he declined admission into the Vulcan Academy of Sciences could be considered a huge example of this, as well as how upset he gets when people speak ill of her, or imply he didn’t care about her. Also, when he asked what she would think if he decided to purge himself of his emotions, it almost seems as if he was asking for her approval.
Her death resulted in a profound sense of grief, regret and anger for him. It’s likely he harbors guilt for not being able to express his love for her more freely (just as his TOS counterpart reveals in the episode “Naked Time”). The fact she’s gone now probably doesn’t help matters. In some ways, his Human half may be what preserves her memory the strongest. This combined with Spock Prime’s advice to put logic aside in favor of doing what feels right may have left Spock with more of an appreciation for this Human half. He even said so himself that Earth was the only real home he had left.
Even so, his inner struggle to feel comfortable in his own skin appears to be ongoing. On one hand, he seems to have learned that acknowledging his Human half isn’t a bad thing. But on the other, his ties to the Vulcan people are stronger than ever after the destruction of their planet, and that was what initially drove him to consider leaving Starfleet in favor of helping build a colony for the surviving Vulcans. Perhaps he believes a way to find himself lies in his developing friendship with Jim Kirk. Spock’s “future self” from the prime reality said this relationship would help define who he was. With this in mind, it’s very easy to see why he decided not to resign from Starfleet after all, instead choosing to serve as Kirk’s First Officer.
There are other aspects of Spock’s personality seen in the original series that hint at a more pronounced duality. For example, he’s scientific, but also displays proficiency in the arts. He gets along fairly well with animals (tribbles and cats, for example), but finds being around children awkward (as seen by his reaction to the newborn in “Friday’s Child”). He can be insensitive to the plights of others (and will admit as much if confronted about it), and yet he’s demonstrated a good bedside manner on more than one occasion (“The Empath” being the most noteworthy one). These attributes are likely present in his movie counterpart as well.