Quickest way of digitising is to download. The quality online is pretty good, but usually divx compressed if you want a good compromise between size and quality (700mb-ish per film) If you want to go full DVD direct rips, then depending on your download speed it might be quicker to rip them from the disks. A DVD rip of just the feature will probably be around 4-8Gb.
Personally I would download and take the opportunity to upgrade to BR quality
I don't know of any wifi nas boxes, but once you start upping the bitrate, I would really recommend going wired anyway...
Personally I leave my imac on 24/7 and use that as the file server.