There are lots of different DM styles. Mine has been honed from 30 years of play. 30 years of constantly second-guessing myself and putting my own style to scrutiny. Much has changed. This is what remains as of now. There is no telling what may change going forward.
I don't DM from a place considering plots and storylines. My consideration is toward a real place with real people in it. They aren't real, but I treat them as such. Things are chaotic and messy. NPCs can make mistakes, be caught with their pants down, fail at plans regardless of PC actions or because of them. Succeed because of them, too. I never consider how the story should end. I don't write an encounter based on how many PCs there are or what the power level of the PCs is. I don't present an adversary of roughly equal power to the PCs to "make it a winnable challenge". Unless PCs draw attention to themselves, the NPCs flatly don't know they exist or care about them. There's no great death waiting for a warrior PC on a bridge saving a fair maiden from a black knight. More than likely death will be from a random encounter and a bad decision made by the PC to not run and/or a bad roll, or a willing sacrifice and their own last stand, their own ending, even if it's just vs 2d6 hobgoblins. I find that more powerful than weird quicktime-style events meant to show the epic awesomeness of their virtue. Current games suck at making PC death meaningful by attempting to make all PC death meaningful. The meaningless deaths add weight to the meaningful ones.
My games seem deep in lore, but there are hundreds of loose threads that, by design, aren't meant to be picked at. You walk on the street and cross over a short footbridge and see a jacket splayed over the side of the handrail. Nobody is around. Who's jacket is it? Why did they put it there? These questions may have answers and may not, I'll even go so far as to say most don't. Sometimes searching reveals something, more often nothing. Not everything leads to adventure. That's how I design. Sometimes a jacket is just a jacket. The world is big and alive and not everything matters, and I find these meaningless things make the things that matter... matter more in the same way meaningless death makes meaningful death matter more.
I generally follow the Rules as Written, because almost none of them pertain to the DM. Example: Troll regenerates fire damage? Yeah, this is a different kind of troll that requires lightning to prohibit regeneration. Yes, the other kind exists too. In the future, maybe you'll spot the difference on sight.
That being said, I don't take the books for granted, as best I can I give the players the game they expect, and where there are gaps I make rulings and discuss with them what the rules should be going forward in the given situation. I decide and write something fair and usually fairly agreed upon. Nearly always players initiate the need for these sorts of house rules. Because again, the rules don't constrain me, they constrain the players.
I also don't fudge dice rolls as I consider it admitting failure as a DM. I don't roll every die in the open, because that could be telling and sometimes a result should be secret until it isn't. Those rolls I will roll in secret. Players do not get that luxury. Any worthy die not rolled in my view is considered to not be rolled. Furthermore any die that doesn't meet my stringent requirement of a lack of bias (gamescience dice or any others that pass a micrometer check for a lack of bias) are not considered worthy. If a player is unwilling or unable to attain requisite dice I will roll for them with mine. Leave your $5 Chessex at home. I don't accept egg-shaped d20s at my table regardless of how pretty they are.
Physical actions can and often do have rolls associated with them. Mental actions, and social actions do not. That is what the players are for. Physical actions occur within the game space, mental and social actions are meant to be at the table. They are an integral part of the experience. I find games with mental or social mechanics hollow and tiresome. Want to give a speech? This is a roleplaying game, give a speech. Want to persuade a guard? This is a roleplaying game, let's hear your attempted persuasion. It's possible I will roll but not to indicate your success or failure, but rather the guard's success or failure in the situation, it's not fair to give them my omnipotent view of the situation.
I ask for minimal PC backgrounds. 2-5 sentences. A name. A brief physical description. I don't want more. Characters, like the world, don't matter if they're not at the table. Sometimes I'll give an assignment. Playing a paladin? Give me 5 sentences describing your paladin order. Even if your character dies, the order continues. Unless it eventually doesn't. Playing an elf? Explain the group you come from. What sort of society are they? How do other elves view them? How do non-elves view them? I have been known to have these elements matter far more than personal elements for characters, outliving their origin of Otto the Paladin or Fernly the Elf. Fernly ran into 2d6 hobgobins. Next character? Oh you want to play another member of Otto's order? Sure. You come from a citadel nearby. How does this sect of the order interoperate with the druids in the nearby forest? I ask these questions to players, sometimes the answer is important, sometimes not so much (seeing a pattern?). Once players give up on trying to guess my story, they tend to try to make up their own, and that's when everything starts working out for them. Or not.
Result: Every conflict the PCs come out on top of is a victory of the players. A victory in spite of a seemingly uncaring DM and rigid adherence to a game system and "realistically" reactive world full of meaningless elements, odds arbited by the best plastic random number generators money can buy. I want players to win, but I will never help them. Cheaters never prosper, and you get out of my games what you put into my games. Not into creative writing projects before the game. Into the play itself. If you invest effort it will reward you. Possibly not this current character, but over time, it will reward the player at the table. That's my goal. Reward players in a way not even computer games can. Helping them to help themselves.
That's why I take DMing very seriously. That's why I have strong viewpoints on any given subject, because I've thought of them all and how to incorporate them into play. Or why I won't. Do I consider this the perfect style? Is it the style I would want to be a player at the table of? Absolutely. Every other style I've seen is complete garbage, especially modern styles. There is an inherent weakness in modern styles because of videogames. Players expect to be the movers and shakers of the world. They expect to be protagonists in their own story. They expect a villain will present itself. Someone to thwart.
Life is more complicated than that, nobody is a villain of their own story.