You'd probably need 6 terabytes (plus or minus a bit) to store all the DVDs you own. A NAS (Network Attached Storage) would probably be the most cost effective, but still expensive. If you're computer savvy you could set up a PC with FreeNAS. Unfortunatly most desktop motherboards only have two to four SATA connectors so you'd need one 8 or two 4 port SATA RAID controller cards.
You would need 8 1TB drives to do 6TB in RAID 5. I would not recommend using RAID 0 even though you would only need 3 drives because if just one of the drives were to fail your 100's of hours of work would be lost. If one drive dies in RAID 0 all data is lost. You could do JOBD (just a bunch of disks) and only use 6 drives but there would be no redundancy and if a drive failed all data on that drive would be gone.
I think 1TB drives are in and around the $250 mark right now. So you'd be looking at $1500-$2000 in just the drives. Add another $1000 or so for a base system with a couple RAID controllers, a good case or rackmount design and hefty power supply. You would be looking at around $2500-$3000 for a system if you built it yourself and used a free OS. If you had to buy a system prebuilt from Dell or other manufacturer you'd be looking at a lot more.
That still doesn't give you a software interface, bu the other products mentioned earlier in this thread should suffice.
There is a company called
PrimeArray that has an out of the box solution for DVD jukeboxing. For something your size it would be expensive.
Note: You'll also want to allocate about a 3 months of solid 8 hour days to copy everything onto your RAID array.