Sauron's motivation to turn to serve Melkor in Tolkien's Legendarium comes primarily from an excessive love of order and keen results that Melkor seemed to accomplish.
Sauron uses the well worn trope of "Only I know what is good for the world" in addition to "Following in the Bosses Footsteps".
For alignment I like comic book characters as examples, they tend to be fairly black and white in that regard. Some are hard to peg for a variety or reasons, but you can always find one solid example of an alignment in comic books. I'll use Marvel because I can think of more characters there that I can explain. DC is way easier with the bad guys (seriously Joker is Chaotic Evil).
LG: Captain America - He's Good, don't argue. Lawful, he thinks the rules and constitution of the United States are it, they define the best way to deal with the world and societies. He'll fight the US government if they're wrong, but he always stands up for The People.
NG: Spider-Man - He's Good, don't argue (or bring up weird one issue examples where Peter's a jerk). Spidey doesn't have any particular attachment to following rules or thinking a particular way of living life is best. He just does what he can to do Good no the cost to himself.
CG: Star-Lord - He's good, don't argue with me. Quill rankles at being told what to do, even if its actually helpful. Rules, order, they get in they way of living freely the way he wants. But he's also prone to letting his feeling take over even when they are going to get in the way. He might have self imposed rules, but they're... flexibile.
LN: Nick Fury - He's all about order - making sure the world keep spinning no matter what the cost. He wont outright kill somebody as more expedient option, but he's not above less than "Good" methods to accomplish his goals.
N: The Watcher - his whole job is to not interfere and just watch (doesn't always work, but on the balance I'd say Neutral)
CN: Domino - She's not a bad guy per se, but also not a good person. As morally flexible mercenary I'm going with Neutral, she has limits and wont go out of her way to hurt people, but also isn't above murder as a way of life. Chaotic is coming from the fact that the whole point is that she just goes and relies on her mutant powers to bend the world the way she needs it to, doesn't do plans as such, doesn't believe in rules, and thinks freedom for all is the way to go.
LE: Doctor Doom - For real, like really. Doom is lawful, he wants order, absolute iron fisted order that he's at the top of, because only he sees what is wrong with the world and only he can fix the world, damn the costs.
NE: Bullseye - he likes killing people. No particular attachment order, rules, or anything that creatures structure, he's willing to work with structure but he's really on interested in payback on Daredevil or getting paid so he can work find without structure and order as well.
CE: Carnage - literally incapable of functioning in any organized way - only goal is murder.