I can't believe no other answers your final and most important question with any detail!
And when looking for an instrument that is the easiest to play, what
should i look for in particular?
You shouldn't look solely for an acoustic guitar that is easy to play.
The play-ability of an acoustic guitar is the only thing that can be easily adjusted!
Nearly all mass produced retail guitars (including very expensive ones) are set-up terribly from the factory and benefit greatly by a set-up from a good luthier. Any guitar, cheap or expensive, can be made to play very well provided it doesn't have any serious defects (eg warped neck, uneven frets) in which case you can return the guitar to the shop.
Buy a guitar you like the look and sound of. These are the properties that cannot be altered easily. Get it set-up by a good luthier to match your specific needs, it will be easier to play and sound even better. (see here for more info: Will a more expensive electric guitar be more consistently harmonious? )
My question now is: are there more things about a guitar that
influence how hard it is to press down the strings? Some things that i
This question is analogous to a combination of a simple beam deflection problem found in all engineering mechanics textbooks and the backpack on a cable problem found in 100 level physics texts. If you want a complete answer try physics stack exchange, All of the current answers are missing key variables. (from my comment).
This is really beyond the scope of this website but I will try to explain the basics in lay-mans terms.
A vibrating string is a physical system. Different strings (even of the same gauge) sound different because they have different material properties.
The same material properties that affect (the sound of) vibration affect how it acts under other forces such as a point load (ie fretting pressure). The main properties are stiffness and density, these properties form the specific modulus. Stiffness affects force required for deflection, density affects mass per length of the string (a value in the frequency of vibration (pitch) of a string equation).
For a given mass per length a less dense string will have a greater area moment of inertia which affects deflection.
Which brings me to the other factor: Which fret you are fretting-
Compare the equations for a centre loaded beam and an intermediately loaded beam here:
As a given force is moved from the mid point to the anchor points the deflection decreases.
Or in other words, the force required to fret increases nearer the anchor points (the nut and bridge). This can be demonstrated easily by bending (which like fretting, requires deflection of the string or 'beam'): Try a whole step bend at the 12th fret (mid point) and then at the first or second fret, the required force is vastly different.
There are other less important points which I've left out. If you want to understand this problem completely I suggest you do a physics or mechanical engineering degree ;-)