Ooooo good, good! Actually, very good, finally we are getting serious.
Digital or acoustic piano?? The eternal dilemma... It depends.
The first painful "note", just to stay on theme, is certainly the neighbors. Knowing acoustic and digital pianos well, I would feel inclined to direct you toward an acoustic one. Why this advice? Because your first piano, the one on which you must train your ear, must be an acoustic piano, in addition to the feeling you must establish with the instrument. I am of the opinion that a pianist can be a pianist without ever having owned a digital one, but not vice versa. However, as I was saying, you always have to deal with the neighbors, especially if you live in an apartment building. In any case, respecting the hours (9:00 - 12:00 and 16:00 - 20:00), barring excessive noise, no one can say anything to you. With a digital, perhaps you could even play later, taking for example a digital piano costing around 400/500 euros, which is not much at all. It is also true that with digital you can do many beautiful things that you can also do with an acoustic, but they require a lot of study, a lot of experience, and a lot of money; I am talking about recordings. Recording with digital is child's play; recording with an acoustic is a very difficult task, especially for an instrument like the piano. First of all, it requires very expensive equipment: at least 2 good condenser microphones with a very high dynamic range (at least 300 euros per microphone), a good preamplifier, preferably valve-based (we are around 1500 euros), and finally a good audio interface (here we start from 500 up to even 4000 euros). Moreover, there is another problem: knowledge of acoustics... Where to place the microphones? Which stereo miking technique to use? How to compensate for the room? What is the right angle for the capsules so that the sound isn't piercing in the recording? How to adjust the equalizer?
Finally, there is the need to use music production software (which also costs money and which you must be able to use: during the recording phase and the mastering phase). In short, as you will have understood, recording a piano is a very difficult and very expensive thing...
With digital, you only need music production software, a computer that you already own, a USB MIDI interface that costs around 30 euros, a sample library of your liking, and very few skills.
However, playing on a digital is not like playing on an acoustic!! Setting the mechanics aside, which in itself justifies the purchase of an acoustic over a digital, there is a problem with the sound. The samples are beautiful, but they are still recordings of a concert grand piano, and it's not like playing on the concert grand itself... Let me explain better. By playing samples, you obtain a recorded performance; you do not obtain a live performance in which you are enveloped by the sound! This is a very important thing. Analog in music is anyway, by definition, superior to digital. (Assuming equal instruments: Steinway D vs. a Steinway D library).
If, however, you live in an apartment with "down-to-earth" neighbors—not to use terms that might cast me in a bad light—it is obvious that you will have to opt for a good digital; otherwise, go for the acoustic. I am sure that Paolo can recommend a good acoustic piano at a low price. I seem to remember an offer he made in a second-hand market for a practically new piano. Get information from him...
Ciao!
PS. How much time do you have to prepare before the entrance exam? It would be a good idea to stay in close contact, perhaps via videoconference, if you want and find it useful, together with Paolo to hear the piece you want to present. Consider that Beethoven's "Moonlight" Adagio is not an easy piece at all. It is easy to read but very difficult regarding touch and tempo. I am sure Paolo will agree with me on this last statement.
