Welcome to the material plane, a world named Shiran.
Here are some of the most commonly known things about this world:
Magic
Magic flows through everything, and those with an affinity for it are common. Seeing someone use magic to do everyday tasks such as sweep or start a fire is common.
There are those in the world who embrace all that is magical, and those that, who might not have the skill to use magic, look at other alchemical, mechanical, or scientific means to accomplish the same thing. Some even would try to meld the science and the magical. Technology is on par with your normal High Fantasy setting, with even some fantastical/modern amenities found as magical items. Example: Record players that play recorded music on crystal discs.
Horseless carriages are uncommon and are done through magical means (though there is someone still having to 'drive' it).
Guns are rare, but not unique. Magical guns (guns that fire magical energy) seem to be more "reliable" and are more common than guns that utilize gunpowder.
Airships are, for the most part, a rare unicorn. In the continent where the adventure begins, there are only 5 known, and each is owned by the respective kingdoms. Those kingdoms use those airships primarily as a way to announce and perform grand posturing. There is another continent, the lower one on the map called the Western Continent, where airships are a bit more common but still rare. They are mostly owned and operated by extremely wealthy people or businesses and used as civil and commercial transports. The manufacturing of airships is extremely costly, and as such to militarize airships has been seen as too much of a risk to do.
There are those in the world who you may run into who are looking to make airships cheaper.
The Gods
The gods of the world are the same ones from the Forgotten Realm. (Keeping spiritual stuff easy to reference). There can also be found other gods from other pantheons.
The 5 major Kingdoms of the Northern Continent
Meolon Kingdom
A human kingdom that is ruled by a King and Queen, and is usually seen as a relatively peaceful, safe place.
Ashicia Empire
A heavy, militaristic region that is ruled by a Dragonborn Emperor. It is said that the Emperor has been on the throne for over 700 years. While they are a military dictatorship, they do not actively seek war, but prepare for when war will eventually come.
Thylelune
A Democratic system that is populated mostly by Elves and Halflings. While the Ashicia Empire is very martial-based, Thylelune is a place where the acceptance of magic and nature are more highly regarded.
Xarin Kingdom
A human kingdom that seems to hold great wealth and prosperity.
Occul'gon Territory
A nation that is predominately non-human like races, ruled by a Leonin Empress, the Occul'gon Territory is seen as a haven for those who are outcasts, or deemed as monsters, but just want to live a simple, peaceful life.
Other major places to note of the Northern Continent
Onyx Crest
An independent city that is ruled by elected officials. The city is well known for its massive colosseum, and a central hub for many different types of guilds across the continent.
Bhildihm
A relatively large Dwarven settlement. Through this one can gain access to the Dwarven capital of Bhan Boldar, the Mythril Kingdom.
Aria
A city on a tropical island. This city was founded on the dream of peace and relaxation.
Old Ashton
A small city that is shrouded in perpetual darkness. Very little is known, and rumors swell about this place.
Runswick
A modest city that is governed and overseen by the Meolon Kingdom. It is here where the adventure begins.
Notable places in the Western Continent
Onahone
An upcoming nation that is yet to be recognized by the world as such. It is where many Tieflings and those that have escaped the nine hells, as well as other hospitable planes, come to call home.
Calilee
A thriving trade kingdom ruled by a sovereign. Here in this desert kingdom, airships can be found and seen in use for trade within the Western Continent, though none has dared to try and fly them across the Deep Coral Sea.
Goldcrest
A city that is known for its mines and metalsmithing.
World-Building
What is on and seen on the map, is the "Known World". There are other continents yet to be discovered. If the party wants to make a goal to begin an exploration of such a thing, they can. They just need the funds and resources to do so. Even in the Known World, there are still ruins, dungeons, and secrets that have yet to be discovered. There are smaller villages, farms, and off-the-normal-path places that the party can travel to if they so choose.
There is currently no "world-ending or world-altering" event going on. The world is in a very stable-looking state.
Game Mechanics / House Rules
Rule 1: Everyone gets an Inspiration point (max 1) after a long rest.
The Inspiration point can be used to re-roll ANY 1 of their die roll. This includes Saving Throws, abilities, damage, or effect.
Rule 2: Drinking a potion / consuming a liquid for yourself is a bonus action.
Rule 3: There is a variation of the Potion of Healing, called 'Healing Salve'.
Healing Salve is weaker than potions, but can just be applied through touch to receive healing. Healing Salve is carefully crafted to be within a special container, where if needed, they can be thrown to apply healing. Throwing of Self-Applying a Health Salve costs a Bonus Action.
Rule 4: There is a new type of Potion called Potion of the Weave that will help restore used spell slots.
These potions work as such:
Using your Proficiency bonus + a modifier, you are given a pool of points to restore a number of spell slots that the potion will allow you to.
Example: If your Proficiency Bonus is a 3, and you drink a Potion of the Weave (Greater), that grants you your Proficiency Bonus + 4, giving you a pool point total of 7.
If you want to restore a level 3 slot, you can by subtracting 3 from your pool.
If you want to restore a level 2 slot, you can by subtracting 2 from your pool.
Levels of the Potions are:
Potion of the Weave - You get your Proficiency Bonus as the total number of pool points to use to restore spell slots.
Potion of the Weave (Greater) - You get your Proficiency Bonus + 4 as the total number of pool points to use to restore spell slots.
Potion of the Weave (Superior) - You get your Proficiency Bonus + 7 as the total number of pool points to use to restore spell slots.
Potion of the Weave (Supreme) - You get your Proficiency Bonus + 10 as the total number of pool points to use to restore spell slots.
Drinking one of these potions costs a bonus action, but you do not receive the benefit until the next round (if in combat). If out of combat, it is "automatic".
Rule 5: Rule of Cool
I like to lean towards the Rule of Cool, where if something that a player is trying to do isn't technically Rules as Written, but it works and fits with the current scenario, let's go with it!
The only limit is that it needs to work thematically with the scenario and the character. If what you want to do is something completely outside of the character, then no, it's not going to work.
Rule 6: Tweaking your Character
Until level 3, you can tweak your character as much as you want; changing stats, spells, etc. Once a character is level 3, the tweaking will need to stop. You cannot tweak your starting gear.