If my iTunes / files are principally stored on the network drive, can I use Time Machine to back up from a network drive to another network drive?
You suspicion is correct.. Apple made TM able to backup to Network target.. not from... it has to be a local disk.
An excellent alternative I use is Carbon Copy Cloner. It is $40 for a license for all the computers in your house.
It backup from anywhere to anywhere.
There is no real resource for NAS from Apple point of view.
The main review site is here.
http://www.smallnetbuilder.com/tools/charts/nas/view
You can click any item on the chart to see the review.
The two main players are QNAP and Synology.. they are neck and neck.. although Apple people often prefer the synology. I have a fake one.. (called Xpenology) since it is open source you can buy a N54L HP micro-server and build your own high power NAS.. but it sounds like you should take it in slow steps.
The big companies all sell models.. Seagate and WD are trying to get in.. I recommend the WD MyCloud. It is not fast .. but have good apple compatibility and for most people will do what they want.. sealed and include hard disk it is a lot cheaper than buying a NAS and then loading it with disks. (WD Red are the disk of choice).
LaCie make a few models and of course Drobo... Have a look at them but the cost and specs I think fall behind the class leaders.
There is no need to jump into a super expensive model.. start small single or dual disk models .. eg WD MyCloud imho is a great starting point. Once you have used it and get the feel of using a NAS.. decide what you need next.
They all offer some sort of cloud operation.. and cloud backup should be possible albeit expensive to do.. A USB drive is the best thing to backup to as the NAS can be setup for auto backup.