Spider-Man to me, is the superhero, he's my superhero, he was the superhero i was obsessed with as a kid, i watched all the episodes of the 90's cartoon as well as Unlimited Spider-Man, the New Animated Series & Spectacular Spider-Man, I played the PS1 and PS2 games, watched the movies, hell, the Ultimate Spider-Man comic was the only comic i read as a kid. Spider-Man means a lot to me, yet despite the multiple adaptations, there is yet to be that one Spider-Man adaptation that I see as the perfect representation, Toby Maguire's version holds barely any of the traits that I see in Spider-Man and even though I heavily praise Andrew Garfield's portrayal, i now see more flaws with it than before. With a new Spider-Man franchise coming to the big screen within a matter of years, i have no idea how Tom Holland is going to play the character, but to be fair, the comics and cartoons have screwed up the character plenty of times. Now this is in no way a definitive list of what everyone's version of Spider-Man should be, this is just my interpretation and how i personally see the character. So let's begin.
The first distinction to make is the difference between Peter Parker and Spider-Man, Peter Parker is the awkward and socially inept nerd that couldn't get a date to save his life, regardless of the fact that he's a superhero, he is still a teenager. This is the key factor that Maguire got right and Garfield got wrong, Peter Parker is a loser, through and through, he has skills, he's very talented, but he's got almost no confidence and will always revert back to who he was before having powers whenever he's around someone from that time period. With that being said, Peter is intelligent, he's a genius, he's also kind hearted and stands up for the right thing, super powers or no super powers, no matter how much he's bullied he won't stay down for long. The mask isn't what makes the hero, the powers aren't what makes the hero, it's the spirit that does.
Then there are his relationships with people, the only people that he's fully comfortable around is Uncle Ben and Aunt May, they raised him and have always loved and respected him for who he is, even his relationships with Mary Jane or Gwen Stacy, there's always that social stigmatism that he's not good enough for them, whether it be physically or emotionally. With Harry he's intimidated by him, there was a point where he always had to rely on him that made him uncomfortable, and eventually that would turn into tension due to the role Harry's father would play as the Green Goblin and then Harry himself. Something that all of these relationships have in common is that Peter hates to rely on other people, he prefers to be able to solve issues himself, he will turn to others for assistance, but if he's not the one doing most of the work then he feels guilty, the worst thing Peter can feel is that of uselessness, when there's nothing he can do to help.
A lot of people mock the idea of 'Great Power Comes Great Responsibility' simply for how broad of an ideology that is and how it can be applied to pretty much every superhero. But look at what is means for Peter individually, Peter initially uses his powers for selfish gains, to get money, to impress people he likes and embarrass people he doesn't. The loss of Uncle Ben is the catalyst that moves him to use his powers for the needs of others rather than himself, some superheroes are born with that ideology (Captain America for example) but others learn it, if you use your powers for personal gain, you will eventually experience a personal tragedy. This is one of the reasons why I hate the storyline 'Spider-Man No More!' which was expanded upon in 'Spider-Man 2' the idea of Peter choosing to give up on being Spider-Man goes against the entire ideology of the character, yes, life is hard, he has to make a lot of sacrifices for the sake of others with little reward, but that's his burden, he didn't choose to be bitten by a spider, but that's the life he has, he knows that, what really shows his strength is that he is able to burden it and keep on moving, having Peter give up being Spider-Man, just to become him again fairly soon, not only is a really pointless story because it doesn't challenge the character but it goes against what he has based his entire existence on. I believe ever superhero has that one rule that you must never mess with or else you go against the core of the character. For Batman, he never kills, for Hulk, he fears his own strength, for Spider-Man, it's that he never gives up, no matter what. Take a look at 'Death of Spider-Man' for how he should be portrayed, even in the face of death, going up against all his enemies with a bullet hole in his stomach, Peter fought till the bitter end, and even though it cost him his life, he saved his friends and family, and he wouldn't have it any other way.
When it comes to actual crime fighting, Peter's main objective should be making sure as many people are as safe as possible, that is always his main objective, and not only that, he will work with others, yes he prefers to go in things on his own because that means less people will be at risk, but he's not so stubborn that he won't acknowledge that he can't always do everything by himself, as long as he is doing most of the work, he won't say no to a bit of help. And don't forget, Peter is incredibly intelligent, even while fighting he usually has 3 or 4 different thought patterns going on in his head at once, one thinking of making sure other people are safe, one calculating a strategy on how to fight the bad guy and the last one coming up with his next one-liner. Which is another thing to point out, Spider-Man is supposed to be funny, when Peter puts on the mask, that's when he can be who he wants to be, the real Peter, when he's Spider-Man, he is oozing with confidence, he always has a joke up his sleeve, he will try and look cool but probably look goofy still, but he will own it.
Something about Spider-Man that I think it would be interesting to toy with is his stance on killing. A lot of superheroes are against the idea of killing because obviously that's the wrong thing to do, but if that's as far as their stance on killing goes, it would actually be interesting to see how Spider-Man would react to something like that. We know why Batman would never kill because that's the only thing that separates him from his villains, he knows how painful going through a loss can be, he's supposed to be a symbol of incorruptibility and he worries that he wouldn't have the will power to come back from an experience like that. Green Arrow firmly believes in avoiding killing when possible, but when it comes to a life or death situation, he's not afraid to take a life if there's no other option. But Spider-Man doesn't have a personal reason to kill, now don't get me wrong, i'm not saying he should kill, but if you wanted to experiment with the character, this would be an interesting topic to discuss, it doesn't go against the core of the character and in the end you can give him a legitimate reason why he doesn't do it. Superman in 'Man of Steel' committed murder and (hopefully) they'll use that as the catalyst to why he doesn't kill, because he's done it first hand and he feels disgusted by it.
Next are his relationships with his fellow superheroes, especially The Avengers, and considering that Peter is still going to be a teenager in the new movie, this is something important for him. Peter idolises The Avengers, they're his superheroes, in particular is Captain America and Iron Man. Peter Parker admires the scientist in Tony Stark, but Spider-Man admires the undying heroism in Captain America. Tony Stark is a genius scientist who has made billions in his life, has been able to help people globally and all without a mask, a life that Peter Parker would love to live, he could do good without putting him or the people he loves in danger. But Steve Rodgers is America's boyscout, there's no denying that his intentions are always pure, he will never give up and is a good role model, the exact type of hero Spider-Man wants to be. There is always that contrast there, he wants to be the best of both heroes but isn't able too, he has to be one of the other, but in reality he doesn't have to be either. He in reality inspires them just as much as they inspire him, his everlasting optimism, his success as an individual and his passion for what he does helps to make them better people as well, keeping them grounded, making them realise the people they save have faces, that they have a purpose and puts things into perspective. You can see more of this in 'Ultimate Fallout: Spider-Man No More' to see just how much Spider-Man meant to the world. But with that being said, Spider-Man is not suitable as an Avenger, he can work well in a team with them when needed, but the idea of being told when to do something and what to do and having to give all of his secrets to a team and they keep secrets from him is not a system he can live by, he's too free spirited and doesn't need someone telling him when someone does and does not need saving, he doesn't believe that the needs of the many outweigh the needs of the few, Spider-Man is always there to help, there is no problem too small.
As for the balance between his personal life and the life of a superhero, this is something almost every adaptation seems to get right. There is always going to be that struggle between trying to have a happy life of his own and trying to be a superhero who is always there to save the day, his personal life will suffer because of it but in the end, I always see that the life of a superhero is more important than the personal life, because again, Spider-Man never gives up. But something that I don't quite understand is his desire to keep his secret identity, I mean I understand keeping it a secret from the public and too an extent I understand keeping it hidden from his fellow superheroes, but why keep it a secret from his friends and family? His logic is that if people found out his identity it would put their lives in danger, thing is, the bad guys find out his identity anyway, his family's lives are in danger and he rescues them. But surely he can tell his family about his identity, it would make them more sympathetic and understanding of his situation and they would acknowledge the risk of being with him and be able to decide for themselves if it's worth the risk, and then when they get randomly attacked by a supervillain, it won't seem as random anymore.
So to sum it up, here's how Spider-Man should be written: Spider-Man's greatest asset is that he never gives up and will always try and save as many people as possible even in the face of death, his greatest fear and weakness is that of ineptness, nothing will make him feel more emotionally crippled than the idea of him being unable to help in anyway possible. Those are the two key features to Spider-Man, not his intelligence, not his comedic nature, those are the cosmetic features, the heart and soul of Spider-Man comes down to his greatest strength and his greatest weakness.