Newbie help how to store and backup iTunes library

It must be an age thing--pushing sixty and I can't make heads or tails out of the advice on the Computer Audiophile site. I just want to move my iTunes library from the internal hard drive on my Sony Vaio laptop to an external hard drive, and simultaneously back it up on another hard drive. I would like for the external drives each to have at least 3 TB of storage. I would like for them to be linked so that the backup drive regularly and automatically updates. And I'd like the drives to work with a Mac Mini, which I'm thinking about buying to use as a music server. If you can recommend specific hardware, I'd appreciate it. Or if I'm going about the storage-and-backup the wrong way, please set me straight. Thanks.
Here' what I've done. Two years ago I bought a Netgear ReadyNAS Duo - works with PC and MAC. There are several models which can handle the 3TB requirement. The ReadyNAS has RAID capabilities which can easily be configured to perform automatic backups to the secondary drives (and tertiary.... depending upon the model). Additionally, ReadyNAS is Squeezebox, SONOS, UPnP enabled should you want to go in that direction. If so, I would recommend the newer models - faster and Squeezebox supported Spotify due to the use of x86 architecture). There's a lot of information on the net regarding both the Netgear offerings and Squeezebox. Good luck. Love the convenience of my Transporter. Always re-descovering my CD collection and new music on Pandora and internet radio.
I own a PC, but I don't think that'll make much difference. Here's what I did...

I bought an external hard drive - Seagate something or other 1TB.
Connected it via USB
Opened up the My Music folder and found the iTunes folder
Opened the hard drive folder
Dragged the iTunes folder from My Music to my hard drive

Everything was copied to my hard drive. Took a while, but it was all there. I also made a copy to another external hard drive as a back up.

After I was sure I had copied everything, I deleted the music in the iTunes folder on my computer. I went into iTunes and changed the location of where my library was stored; I use a pc, so it was E/iTunes.

Never had an issue. I'm sure there are subtle differences with a Mac, but I'm confidant it's the same basic formula.

Whenever I rip a new cd, it goes straight to the primary hard drive. I drag and drop the new albums to the backup drive after a few albums.
I did much as Kbarkamian. I bought two external 2TB drives from Other World Computing. I copied my iTunes folder to one of them using a FireWire 800 connection. I then daisy-chained the second drive to the first and made an exact copy using SuperDuper.

Then I opened iTunes with the Option (alt) key held down. iTunes asked me to choose an iTunes library and I directed it to the one on the first 2TB drive. From then on iTunes has opened automatically with this library.

Whenever I add new music to my iTunes library, I back up the changes to the second external drive using SuperDuper.
For the most part, my understanding is that external hard drives do not play well with both PCs and with Macs -- you sort of have to decide in advance which way you are going, because the hard drives have to be formatted differently for the two operating systems. So you may want to get the hard drives and the Mac Mini all at the same time, and do this all at once.

Assuming you have either Snow Leopard or Lion set up as the operating system on your Mac Mini, what you propose to do is relatively straightforward.

First, you should select hard drives that use the Firewire 800 interface (Apple sells several 3T models with Firewire ports, from various manufacturers, through its online store and in its retail stores). You can connect the drives to the Mac Mini "in series" following the instructions that come with the drives themselves. Both will be visible on your desktop.

Then, copy your iTunes library to one of the external drives (to move it from a PC, you may have to either use a network connection or burn your iTunes library to a DVD-R, or purchase PC-to-Mac conversion software -- I'm not sure what the right approach will be -- the Folks at Apple's Genius Bar can help)and then re-set iTunes on the Mac Mini to recognize the copy on the external drive as your iTunes library (there are instructions on how to do this available through Apple's online support -- or, once again, you can get instructions from the good folks at Apple's Genius Bar). When you add new music to iTunes, it will be installed on the copy in your external hard drive.

Then, set up Time Machine to use the OTHER external drive as your Time Machine backup drive, and configure it to back up the iTunes library on the first external hard drive as part of the Time Machine backup process (this is easy to do using the Time Machine software interface on the Mac Mini).

While I'm not using 3T drives, this is exactly the setup I'm using at the moment for my photo library, which had gotten too large for the hard drive in my MacBook Pro. I have the libary on one external hard drive, and then have both the MacBook Pro and the photo library being backed up onto a second external hard drive using Time Machine. Works just fine.
Rdavwhitaker's warning about the different formats required for MAC and PC is useful and his advice is good. If the OP wants to understand why it matters and what to do if he takes it on himself, there is a clear and easy-to-read explanation on this page by Matt Neuberg.
Above still a little fuzzy to myself. Can itunes be backed up in the cloud. Such as itunes, icloud?
iTunes, or any any other data, can be backed up to iCloud. Just remember, though, that Apple only gives you 5 gigabytes for free; if you need more space than that you'll have to pay for it. Also, backup will only be as fast as the upload speed of your Internet connection. For most consumer connections, the upload speed is pretty slow, meaning that first backup can take a long time.