Here's how I would do it. It's not going to be a complete step-by-step solution, but hints and tips on what to Google.
AvoK95 wrote- To print something from anywhere in the house, by having my printer be shared by the netbook.
The simplest printing management package on Linux is called
CUPS. Learn to configure it, it will do what you want.
- Add/delete files wherever I want in the hard drive for storage
There are plenty of file sharing solutions. The easiest would be to set up something like
VSFTP.
- Use the Bluetooth to automatically connect to my phone when my phones BT is turned on and automatically stream my phones music to a sound system the netbook will be connected to
No idea how to do this. But I would look into
DLNA. It's fairly straightforward to set up, but it might not work exactly like you describe it.
- Have remote access to the netbook via TightVNC or something (Though not a big deal)
You can probably setup something like
Vncserver. But remote access on linux is rarely done graphically, it's usually done in the terminal. Look up
SSH.
- I want it to be a web-server for my internet connection, so that it caches my downloads of the week. So that whenever I download updates on my phone, my brother and mom don't need to download them again, instead have it downloaded from the netbook's internet cache. Same for Windows updates and videos ofc.
Squid will do what you want for web content (everything you get in your web browser). I don't know if you can configure it to cache phone and windows update. It's an area worth exploring.
- Share the Wi-Fi connection to the LAN port to connect it to an old original Xbox which is going to be used for streaming movies on an old CRT TV I got in my room.
If you install a graphical interface on your Linux box, it's easily done with NetworkManager. If not, check out
Wicd.
- Being able to scan something on the netbook and have it automatically be saved by a press of a button in a folder where I can get the file via network.
I've never tried scanning anything on linux, but I hear it's easy to do.
- Have it be on all the time. So that when I close the lid, it doesn't go to sleep or something
Depending on the system you use, you will have different "power management" options. Use them to configure the netbook not to sleep. That being said, be warned that the netbook's hardware really isn't made for continuous prolonged run, and you will most probably run into hardware degradation pretty fast.
What I need is, help with Linux, since I have minimal experience with the platform.
I strongly suggest you spend some time learning how to use the linux command line to go through your file system, launch/stop applications, install/remove programs, edit configuration files, ... It may take some time in the beginning, but it will make your life so much easier as you start working on configuring all the above programs.
BTW, only the netbook will be running Linux, every other PC in the house will be running Windows 7 and 8.1.
Don't worry. Using linux on the server when all the clients are running Windows is a very common setup.
So, first things first. Based on my requirements above. What distro would you recommend?
It doesn't matter. There's no wrong choice.
A lot of the documentation I give you come from the wiki of ArchLinux, a funky distro. It's a bit more difficult to set up at first, but it has one of the best documentation of all software projects I've ever seen. Ubuntu and Mint are popular choices among newcomers, so you'll find the most tutorials aimed at beginners. Personally I am most familiar with Debian, so I could help you best on Debian, but most of what you learn on one distro will translate pretty well on others.
Can I use Debian as a regular consumer OS as well when I need to?
I don't understand that question.