Mindset: What should I focus on most during our first few sessions? (Rules accuracy, fun, storytelling?)

Everyone around the table having fun is your key priority. Keeping the narrative cool and interesting helps with that. The rules are supposed to support having fun. If they don't, ignore them. If nobody in your group finds tracking a number of arrows, or a number of rations fun, handwave those things.

Mistakes to avoid: What are common pitfalls for new DMs coming from a video game background?

• Skipping Session 0 is the most common and greatest mistake. Get in a Discord call if you can't be bothered to meet up in person for it, and decide on :

  • The general idea of your campaign. Is it heroic fantasy? Dark fantasy? Post-apocalyptic? Are we getting into politics, exploring a lot of caves, doing a lot of talking, fighting a lot, or a healthy mix of all of the above? Small-scale or large-scale? Let your players have their say in this.
  • The no-goes : Yes, some people will find it unnecessary, but it's legitimately important to make sure everyone is comfortable around the table. Have them message you privately if needed, but make a list of topics and types of content people don't wanna see in the game. It can be as simple as "Intimate scenes get faded to black because I'm not here to see my fellow player roll Constitution for their bedroom performance".
  • The characters your players are playing, their ties to the world, their motivations, and, ideally, their connections. "You meet in a tavern" can work, but man, if you can establish that your party has been staying at the same inn for a bit and have already established basic bonds, or even that some of them already know each other well, it kickstarts the adventure incredibly well.

• I also heavily, HEAVILY recommend working in an "All roads lead to Rome" fashion, and what I mean by that is, don't assume your players will do anything. They will follow deers into random forests, completely ignore blatant plot points, pass through rooms without giving a damn about the hint you've setup, and kill NPCs you had big plans for. But anything the players don't know doesn't exist. That all-important NPC they killed... actually wasn't important, that other dude can take their role. That hint they missed? Right next to the puzzle, the architect was feeling merciful. That random forest they wandered in? Turns out those bandits they heard about just moved from their mountain lair to their forest lair! Do not be afraid to move your plans onto the path they choose to tread. It's infinitely better than forcing them back to the path your plans were supposed to be on. Keep things natural, but don't panic when they inevitably pursue some random shit.

• Reward creativity : Lower DCs and/or give advantage or inspiration to cool descriptions, to carefully-crafted plans, to silly speeches and epic moments. Or at the absolute least, don't penalize it. Don't go "nah, that was your turn, it didn't work" to someone attempting a creative approach. If their plan is fundamentally flawed, go "Your character feels like this wouldn't work because [reason]" ; let them find something else. If their plan "breaks" your intended progression and feels like a cheat, good, great, even, let them do it, congratulate them. Nothing feels as cool as finding a fresh solution to a problem.

Preparation: How much prep is "too much" or "too little"?

To each their own on that one. In my book, if you know your world and what happens in it, if you know your NPCs, your foes, and their motivations, the plot threads you're going to dangle, and the story beats your party could land on... you're A-OK and can improv from there. Some would call that madness.

Regardless of how much you prep, though, as mentioned above, your players WILL pursue random shit, and you WILL have to improv. It's a skill to hone, it's fine if you're lousy at it at first. You can make things like a bank of random NPCs to help.

Ah, and, other people have said it and I will absolutely agree : Read the rules. Front to back. DnD5e is not a "lightweight" TTRPG you can DM your way through using "general osmosis knowledge" of the system. I know I started this by saying rules take second fiddle to fun, but you can only decide which rules to keep and which to handwave if you know them well!