So I watched a video by Overly Sarcastic Productions that covers pretty much everything. (I'd provide a link to the video but i don't know if it's allowed) The video itself only explains what he does throughout his journey all the way up to being sealed away by Buddha under the mountain. What it doesn't really cover is what kind of personality he has. I mean it kind of does, through his actions, but not his actual character. I plan on making a character based on him in my next original fiction project (gotta finish my current one first) but while I could create my own version since his character is a version of him where he actually escapes said mountain imprisonment. I want to be as loyal to the source material as I can.
A quick search revealed this: Characterized by his short temper, impatience and proclivity towards anger, Sun Wukong is one of the most important and beloved literary figures in Chinese culture. Seems like a simple baseline to riff off of.
There are also a few Journey to the West/Monkey King tv shows available on YouTube. I think the one from the 1980's probably represents what most people view Sun Wukong's personality: arrogant, sometimes mischievous, but eager to defeat any bad guys they encounter.
Would it be interesting to have him aware of Journey To The West itself? Like reading the actual book? In this particular world, it wouldn't be impossible (It's a high fantasy setting that takes place in 'our' earth, eons after being destroyed) for him to come across the book. In fact, many characters in the story are inspired in this way. It's an actual plot thread in the story itself.
Why not? There's tons of books (Neil Gaiman comes to mind) with mythological beings arriving in "modern" settings fully aware of their own mythology and all the irony that comes with it.
I might go with that, partially because it's an actual plot point. (as in the plot is literally that, a 'fictional' reality coming to grips with the state of the 'real' world) I feel like it'd be an interesting topic, since many characters are dealing with grief. Heck, the villains think they're grief itself, and four of the five stages also think they're the four horsemen. (even though at least two are women)
Just read the book, or at the very least the beginning (which I guess would be considered a prologue today) as it deals with the early exploits of Sun Wukong and gives you a sense of his personality right away (though he continues to develop throughout the novel). It's buckets of fun, there's no reason not to read it; it's also a great introduction to the Chinese popular religious cosmology. Failing that there are plenty of abridged versions, comic books, cartoons, movies, etc. available. If you aren't interested enough to do the basic research like that, why use the character at all? Tolkien, Gaiman, etc are great in part because they actually love reading mythological and folkloric source texts. Do your part to combat the wikification of fantasy literature.
Is Sun Wukong the Monkey King? If so here he is, depicted in all his majestic simian glory by one of my favorite artists, Katsuya Terada (AKA Terra): Spoiler: Space Saver
Yeah, that's him. It's a little more menacing than most modern depictions. That's his staff that weighs like 30,000 pounds but can shrink to the size of a straw. The small crown or tiara on his head is how the Buddha and the Monkey King's master (a Buddhist monk) control him during the quest as the Monkey King often wants to abandon the enlightening journey and just kill the monsters and finish the quest.
While the full Journey to the West is an absolute monster of a book/series, I quite enjoyed 'The Monkey King's amazing adventures' which is an abridged translation by Wu Cheng'en and Timothy Richards. Much easier/cheaper read and should give you plenty of material to work with if you want to use Sun Wu Kong as a character in your story.