If you have a desktop, just throw in an extra 500 gb hdd, or a TB one, or whatever. For backup, copy it onto another disc and put it someplace safe. A fireproof safe, or a safe deposit box, or just a shelf out of the way somewhere
Also, if you're doing video dvds,
Handbrake with high compression 264 settings can drop the file size to between 25% and 33% of a straight vob/mp2 dvd video file at as near to no degradation in quality as makes no difference for my purposes. I've been transferring old episodes of B5 and the like, and I'm able to drop file sizes from about 1.8-1.9 gb/ep to about 550 MB. (Handbrake encode and analysis settings all to max, or a bit beyond on the encoding ones that have minimal effect outside the recommended range because that makes cel animation go smoother, 2pass w/turbo @ 1250 kbps, takes a bit of time to do the encode, CPU dependant, I've got a two-year-old midrange AMD processor, and with my crazyhigh settings, encoding time approaches roughly 3x running time.)
Since I started the project I've moved two sizable boxes of DVDs to long-term attic storage. Everything's kept in a network shared folder which I can access from the smart tv box in the living room (which can handle the BD quality stuff I got when I ran my BSG discs through
Makemkv - Don't try this at home unless you've got 750GB spare for the four seasons worth... 6.8 GB/episode adds up fast.)
As for the NAS concept, I (being that guy on the internet) recommend putting together the hardware (PSU, Mobo, CPU, RAM, enclosure, and HDDs) and rolling yourself a lightweight linux fileserver. Close control, much more potential for personalized combustibility, the ability to offload the above mentioned handbrake compression process (depending on how much horsepower you want to put into it...) and blah de blah blah that I'll be glad to go into detail about if you actually care.
And my agreement with Nuke should go without saying. Don't try to set something like this up over wifi. (Stream to your laptop, sure. I like to stream video files to my netbook while I sit in the hammock in the summer, but that's one file at a time, as I watch it, not bulk transfers. It'll take forever to set up if you're not jacked in...)