1) Random encounters.
From my time as a player, I remember them as the least fun part. Even if something nuanced happens, they always felt like a delay before the main adventure continues. That being said, removing them (chance of them happening) was worse since this reduced the riskiness, and thus the importance, of the travel. I tried giving some exposition and describe the road, forest and stuff, but it doesn't do much to address the issue. What in my opinion made things better is preparing a list of special random encounters based on the player's background. So instead of random combat, the party will meet something related to one of the characters. This also felt like a much better way to expand on their backstory, then trying to tie into the main plot. What may end up happening, is by encountering something from their past, players may weave it into the core narrative themselves.
2) Assets & Initiative order.
Aside for DM screen, core rulebooks, Dice and a Notepad I don't have many tools. Well, recently I did make that grid map you see above. But one improvised thing that helped streamline the combat was colourful round tokens from another board game. Basically, assign each player colour from the tokens you have (can be any colourful set of objects).
In my case:
Rogue - Green
Paladin - Yellow
Warlock - Black
Wizard - Blue
Cleric - White
Enemies - Red
And use them to track, whose turn it is. I flip them to remember that the person took it's turn already. I keep them so that everyone can see. This helps with planning. If my friends have board games I cannibalize them (with permission) for additional dice, tokens, figures, etc. to show where enemies are. I sometimes swap tiles to tell which enemies are injured, affected by something, etc. Azul has nice tiles, we fought them a lot ;)
3) Characteristic decisions XP.
I'm not sure how players feel about it, but when asked about how I reward individual experience for non-combat activities, I said that in a big way it depends on what is important for a character. If Wizard who is obsessed with knowledge is taking unnecessary risks to learn something about certain magic, that would be it.
4) Music from Skyrim.
Unless I know specifically which music/ambience I want, I'll just put some Skyrim OST on YouTube.
5) Digital tools
There is also a cool https://avrae.io/ integration for Discord that I haven't used yet but it looks interesting.
I also used Dice Ex App (iOS) for when I need to roll like 10d6 or something for an army of enemies (Azul tiles). It has a D&D calculator and other features.
I bought a Reroll app back in a day to create pixel art of the character but never used it. I think most of the time players aren't even sure what their characters are wearing - I don't think that is a problem though, seems to be ok.
I must add that one of the most charming and inviting things about D&D is pen & paper. Learning that a sheet of paper and a pencil that is usually associated with tedious studying or work can be used for something so fun is the true magic of it all.
6) Core mystery
Not every adventure needs to be about solving a great mystery. In D&D everyone creates their own story in their very own world. But I often build everything around something that I know and players don't. Some secret, knowing which would have ended the game there and then. "The solution was inside of you this whole time" kind of thing. Not only in general but in every given situation I think to myself "What is it about this room that they don't know?" and then say: "You see a bookshelf with flowers and various organic things there, some crystals. There are large books, one of which is open and page is partially filled with text. Ink is right next to it." - this would be what I say if I have decided that the room belongs to a Wizard.
7) Poker face
The "core mystery" method I described above pretty much solves me my creativity - basically just asking and answering questions. You will even find the official D&D book "Dungeon Master's Guide" be filled with various tables to roll and pick some catalyst for your narrative. One thing that remains to be exercised is the poker face. I often unintentionally give it away when players are doing something unimportant or not something that can solve the challenge or feels not interesting to me personally (because I know the solution). For example, they want to ask about the previous mayor of the city. Me: "You learned that he was just a normal mayor, nothing special" - screams "He is not important!". Maybe this is ok, who knows. I actually don't have a good solution for this but it is good to keep it in mind.
While the world of D&D can serve as inspiration itself, I wouldn't be surprised if most DMs put third-party themes into it. D&D is extremely inclusive, your Ktulhus, Pennywise, Aliens & Predators can easily be imagined into it. Some of those I like:
Magnus Archives (YouTube, Podcast) - it is really good scary but immersive stuff.
Marvel comics - no introduction needed.
Critical Role (YouTube) - obviously no better inspirations then actually watching people play. Not always in the mood to watch it though.
Shut Up & Sit Down (YouTube) - Not D&D but gets me into a right state of mind.
9) World of D&D
Not just interesting but also practical. If the story were to take place in our real world, any supernatural event is expected to have a shattering effect on the psyche of anyone witnessing it.
"You are coming back from groceries store, checking your Instagram feed and suddenly a dragon flies over you"
- it is hard to imagine how a rational person can react to this, but shock and panic would be the first step. Not something players often want to reenact. Default assumptions of D&D are that magic, monsters, gods - all exist and inhabitants are aware of it. Magic may not have a tangible presence in the day-to-day life of regular people, but when something does appear, it would not flip anyone's world view. While having a strong role-play element, D&D does a lot to make it as natural as possible to envision oneself in your character's shoes. Understanding why rules and world are the way they are helped me to feel comfortable with classic tropes and use them to my advantage. Everything that lets players make assumptions makes the world more vivid in their mind.