Hi i'm totally new to this forum and also so new to arduino tech.
Welcome!
The idea i had was to create my own data collection buoy, something really simple (at least in the beginning). I would like to take measurements of the free surface oscillation on the field (on the water surface), with some kind of a micro-controller and data logger system.
Good idea, but is there not something out there that already does this? It sounds like the kind of idea that must have been implemented by somebody already.
Is it possible to obtain the free surface variations using arduino hardware?
If what you want to measure is acceleration then yes, it is possible and you have the right kind of components. You will, of course, also need a waterproof case

Who do I interpret the reading of an accelerometer?, cuz wave height is in meters!
Integrate! The integral of acceleration is velocity, and the integral of that is distance. Then, confront reality in the form of noise and start playing with filtering (but you can do that with Matlab after the fact if you just record the raw acceleration data).
Is it possible to create an autonomous device, that last at least for 3 months taking data each hour?
Sure, you just need a big enough battery.
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The
QuadRAM shield: add 512 kilobytes of external RAM to your Arduino Mega/Mega2560