Hello everyone! Ireally need to thank you all for your answers: with your advice I managed to achieve two or three complete but really different solutions:
1) @Frieza: I tried LogmeIn and it's great: the only downside is that on Android you have to install a client app, but that's not real problem. The "problem" is that, being a no-conf program, doesn't make me learn much However it's so easy I'm definitely going to use it: thank you Frieza!
2) @Debguy: sorry but I'm not sure if I got the point in your message (don't know english perfectly): however if you are asking if i'm paid to do these things: absolutely no (I'd love to! )
As I pointed out before I'm a student (18 years old) trying to dig into the Linux world (mainly networking), learning new things and so on: where I wrote "work" I meant "school or some place where I could be outside home" and no, I'm not paid to attend school (I'd love that too)
3) @wpeckham: I really owe you one, because your suggestion led me to a great discovery: my router can be configured to run a VPN IPSEC server to which I can connect both from my PC and form my Android. The server is fully configurable so there are lots of things to learn.
Moreover, before discovering this, I tried to configure my server to run VPN and, despite the fact that i couldn't make it work, I learned lots of things by trial and error. Thank you again!

I consider this thread solved even though I couldn't accomplish my third (not strictly necessary) point ("routing only LAN connections and connecting to Internet directly"): maybe I'll sort that out too...