Some people call Percy unpredictable.
Some call him stupid, or a seaweed brain.
Percy himself just wants to be a normal kid eating blue dyed pancakes and sweets his mom makes him from time to time.

Even though he's been through everything a demigod could ever go through and more, he always mentally comes back to his home with his mother whenever things get hard. Their closeness gives him as much peace as it does nerves, but but thinking of her always gives him strength. That's how it was at first, anyway -- until he met Annabeth, Grover, Nico, Thalia, Tyson, and everyone at Camp Halfblood. Even though he was dragged into a crazy life, and doesn't exactly want it, he'd rather protect the people he cares about rather than just walk away.

At the end of the day, that's the core of Percy.

His loyalty is remarked on being his Achilles heel -- specifically for Grover, Sally, and Annabeth. Especially Annabeth. Though she can take care of herself, he always gets even more specifically angry on her behalf if anything happens to her. She's been his constant, sarcastic companion since he even found out he was a demigod.

But as I said, it's also kind of a curse. His loyalty for others will make him have very little regard for himself. The gods themselves remark on the fact that it'll get him killed. A lot of his regrets are tied up in that too, feeling as if he could've been better or done something more to have not gotten some of the demigods killed in the war. It's something he thinks about often, even though others tell him that there's nothing he could've done differently.

Percy's close other friend Grover and his half-brother Tyson, he'd gladly walk into the fire to help and protect as well. He went on a whole quest to get Grover back when he got captured by the Cyclops, and while Percy's relationship with Tyson was strained at first, he began to also care for him fiercely. Even to the point that Percy would get emotional on some Iris-messages after Tyson had gone to work in the Poseidon's forges.

The gods' opinions on Percy varies. Poseidon's proud of him, at least there's that. A lot of the other gods believe he's too unpredictable and it scares them. Because he's so powerful, and fierce in quests and fights, they get concerned about what he might do to Olympus and their reign in New York. Some of it is because of a prophecy that was told about it, the rest is because he can and will backtalk and fight every single god, mythical person, or human that tries to tell him no or get in his way. Hell, at 12 years old he figured it'd be a good idea to fight Ares because he got pissed off.

Ultimately though, even if the gods were worried about him destroying what they'd built, all he cared about at the end of the day was the other kids. The other half-bloods that aren't as lucky to have relationships with their parents or feel cast out. He calls them out on their bullshit to tell them exactly why Luke turned to the Titans and why Thalia became a Hunter of Artemis. Even though he could've had immortality, he used his favor with the gods instead to demand that they give the other kids their attentions.

Moving on from his relationships, another one of his biggest weaknesses (that he will outgrow somewhat with age and training) is his lack of attention span. Every demigod has dyslexia and ADHD -- the ADHD is attributed to great battle reflexes and the innate awareness that comes with the dangers of being a demigod. In this case, he's very much a kid with attention problems for the first couple of books, or just prone to doing reckless and sometimes what others would call stupid things. He begins to come more into himself as the series goes on, and even though he's still super headstrong and leaps before looking, he becomes more grounded. Mostly because Annabeth is there to tell him he's stupid...and he does try to listen to her. Tries.

Another thing he develops is an ability to lead. While he was pushed to the side for more "leader-like" characters like Thalia, Annabeth, and Clarisse in the beginning, he comes into being a leader under scenarios that make other people freeze. Even when Zoe freezes up in Titan's curse with fear, he's able to try to drag her through it and come out the other side (mostly) unscathed. He's not afraid of challenges and keeping himself and others alive, which is mostly why he puts himself in these situations where it calls for that he takes charge.

On the flip side of all of that, he can be pretty dumb as far as basic social interaction and common sense is concerned. It's how he earned the title "Seaweed Brain", after all, because of getting in strange situations and seeing things that are right in front of him. Some of it he attributes to his ADHD, but at some point he's just trying to make excuses. He's usually pretty oblivious to the way people feel about him or if they're trying to make a social cue to him, often overlooking these things for whatever else may be going on at the time. The obliviousness oftentimes gets him into strange situations, like ending up in Medusa's shop or being swayed by cute girls that ended up turning him into a guinea pig.

Despite everything he went through and will probably still go through as a demigod, he's still a silly goofy teen with a heart of gold and a short fuse for anything that might happen to the people he loves fiercely. The only problems is that he has a extreme fear of flying and doesn't like to be told "no", but everyone has a few problems with themselves, right?

I think that Percy could fit into either armada, but at this point I'm leaning more towards Corsair. He's very adventurous and impulsive, because what is thinking about your decisions before you jump into them? And, as much as he can work in groups, he usually ends up running off by himself doing some dumb shit in the middle of a fight or in an intense moment.