library vs media folder on shared drive

I've read so much on this that I'm just frustrated at this point with something I would think would be easy to understand. For me however I'm still confused.

Background:

I moved all of my media to a network drive (it's a Time Capsule) in order to free up space on my laptop and also make it usable across devices. This seemed easy enough by simply copying it over and changing the location of the media folder in Itunes preferences.

Here is where I get confused - what about the Itune "library" information?

Many people use these terms interchangably but they are different. Library is different from media folder.

I copied my old Itunes library files to the Time Capsule as well and pointed Itunes there but it's in a separate folder than the media. When I did this and pointed Itunes to it it created a new Itunes media folder in the library folder but it had nothing in it (I guess I may delete it?). I then changed the media folder in preferences back to my orginial folder which is also on the Time Capsule. In doing this it is going through a really time consuming organizing excercise even though everything should have already been organized.

I am wondering if this is a good way to do this or if there is a better way.

Can I use that exact same library on other laptops? Would it be better to have library's local to each computer but just share the same media folder?

I know I can use the same media folder but not sure about the library.

I thought maybe I'd want to use the same media folder AND the same library folder for multiple laptops which is why I put both on the shared drive. If this is not a good idea please let me know.

I would like to keep things organized so I could add new music from any machine and have it go the main master media folder for use on whichever machine I want.

I know this is long winded but here is what I have now:

Local computer -just has Itunes - no media and no library files here

Time Capsule - has a master media folder (inside are all of the apple subfolders for music, movies, etc); also there is an Itunes library folder (inside is an artwork folder, empty media folder, library databases and genuis database)