Say you have 400 albums, and say they average having about 500MB of uncompressed data on them (it will depend on how full all of your CD's are, whether some are singles etc.) That means you're looking at about 200GB of compressed data, which isn't a actually all that much these days. It will take a while to burn them all, but it can be done in a couple of days.
So a lossless format (say FLAC) will compress those CD's to about half their size, so you're looking at about 100GB of data after you've ripped and re-encoded your entire collection. Even these days with hard drive manufacturers taking a production hit from floods in Thailand, you can get a 500GB hard drive for about $100, or a 1TB for about $150. Given a 400-disc changer may cost $700+ new (and might sell for $200 used), there really isn't any reason to need them any more. You can buy an entire computer with plenty of storage for less than the cost of a huge changer like that...
I would recommend getting either iTunes or Zune software, and going to work ripping your entire collection. I use MS's Zune which can rip to WMA Lossless, its organization of the albums in a directory structure is easy to navigate even outside the software (sorted by Artist, then album) and it will automatically detect and add all of the CD's information including album art, artist, album name, track numbers and names, etc. Software like iTunes or Zune also has the advantage of being able to rate songs (give songs you don't like thumbs down and they won't play any more) and you can have it automatically generate playlists based on music genres or similar artists.
Then if you want to take it one step further you can share that music collection across your network and access it on any computer, and you can upload up to 10,000 songs to Google's cloud-based music service and access it with most internet-enabled devices including smartphones (Granted the songs on Google Music will get re-encoded to a lossy format once its up there). Most importantly, if you get a large iPod and use iTunes, you can carry your ENTIRE music collection in the palm of your hand (while retaining lossless compression)!
160GB Ipod: https://www.amazon.com/dp/B001F7AHY6/?tag=pfamazon01-20
Welcome to the 21st century, it's nice here ;-)