For beginners, Free Play mode may be the safest option as it has the least amount of restriction/is the easiest game mode. Unlocking all countries is also not a good option and neither is Scenarios, especially just starting out..

1. Picking a Country
When you're going to pick a country, picking one with a stable/average population and a little amount of cities will be the best choice. Going for a small amount of land to cover is also good.
This means your airports will not be full right off the bat and your routes will be cheap to make and it will make transfer of passengers quicker as the routes are shorter and take less time to complete.

This means China and India will have a lot more passengers and Russia's routes will be very expensive, which is not ideal for early game as you will not earn much until you have unlocked several countries and most of their airports.

2. Spending In-game Money
There are many ways to spend in-game money, and they can be affected by events (explained later on) and how many times you have done them.

2.a. Upgrading
There are two things you can upgrade; airports and planes. Upgrading a plane will make it more expensive to continue upgrading that plane, and this happens with airports too.

Well, what does it do and why do you need to do it?
For airports, you need to upgrade them because they will become full. A full airport will give you a status that will cause you to lose 30% of your income, and this can lead to more full airports that you can't upgrade. Upgrading airports gives them more capacity, meaning they can hold more people. If you can't upgrade an airport but can add a route listed in your top routes, please do that instead.

For planes, you can upgrade them if they are constantly full. Upgrading planes gives them more capacity, and they will also complete routes faster. The max level you can upgrade a plane to is 6.

2.b. Unlocking
Looking at countries, I've already mentioned in [1] Picking a Country that choice of countries can make a difference to how your game plays out. It'll be the best idea to pick a larger country if your first country was smaller, and connect all the airports together in the new country. You can connect the capitals together, but if your airports are full because they want a route that doesn't exist you can also add that route.
Unlocking a new country will become more expensive the more countries you have unlocked.
Unlocking airports will not cost anything and they will come free of charge, which will be announced at the bottom of your screen in-game. See [2.a.] to find out more about airports and planes travelling along routes.

2.c. Affecting Factors
Why is this section so long!?
Well, there are many factors to your early game, spending in-game currency, and picking a country. The main factor that can change in-game currency transactions and how your save plays out after picking a country is events. This is a complex section, so you may ask for me to break anything down in the comments.

Events can; block a country, remove planes, add planes, upgrade planes, downgrade airports, give you money, increase visitors to a city or country, increase ticket price, etc. There are many things it can do.
Lots of these things will require spending in-game currency and you need to read the event through to make sure you won't go into debt and to see what it's going to effect.

This is the main section about playing the game covered, and it's all you're going to need to begin playing. This may seem complex when it's explained but it isn't when you look at it ingame.

1. Full airports
You can avoid this if you have the money to upgrade it. You can also add more planes to a popular route, add new routes that haven't existed before but people want to travel along or upgrade planes along a popular route! The reason to avoid this is that it means less people can buy tickets, decreasing your income as well as taking away 30% of your initial income.

2. Debt
Self-explanatory. If your money is not above the amount you are about to spend, do not spend the amount until you have more money. Number 1 may affect your income as explained, which will make going into debt harder to avoid. Read every single event through unless you know what it will do by the picture or a few words that you have read, as they may send you into debt later on or immediately.

3. Expensive routes
Also self-explanatory. This can lead to 2.
Your routes will get more expensive the longer they get, and you will need to upgrade your planes to fly them in a shorter time. You can also add more planes to get more passengers going along your route at once, but both solutions can also lead to 2.
If you need to cause this in order to avoid 1, please cause it sparingly as it risks your save a lot of the times.

4. Unlocking a country with no spare money for routes and upgrades
Very self explanatory in the title. If you cannot make new routes, your airports will fill up (leading to number 1 if left long enough) and if you cannot upgrade your airports or make new routes to avoid number 1 this can risk number 2 and in turn risking your entire save.
This number will not cost anything immediately if you are earning enough money, so it is safe to do this later in your game.

Scenarios will appear in any shape or form. They offer a challenge to more experienced players, basically putting them in a situation that is different from what is reccomended or has a special 'scenario' (hence the name of the game mode)
Scenarios will often include:
Blocked international travel
Large population countries (see previous section)
Large countries
and more.

This section is short as I am more comfortable playing in free play. Scenarios are very complicated.

Reccomended playtime to begin scenarios:
Good at the game: any playtime! It depends on when you feel comfortable to try it out.
Bad at the game: More then 10 hours. It is reccomended to find a guide on scenarios that goes into more detail then here if you fall into this section!