I'd give a strong consideration to using AppleTV or similar device, and going that way.
Essentially, get a large hard drive. Use Handbrake or similar to rip the films to hard drive (about 1GB per film, and assuming you don't care about menus and other special features much; keeping full quality DVD is still impractical with this many DVDs), then get a small computer to play them.
XBox Media Center is apparently very good for this, and there are other free software versions too, similar in function.
You can install XBMC on an XBox, or a computer -- Asus EEE Box are nice small ones, that it should run on. Connect your hard drive to this, and it'll work.
AppleTV does much the same thing, but has a better interface, good remote control, and will grab films from computers round your house too. But costs more.