Right. In which case, you've got a few options. If your PC has an optical out, you can take that directly to an optical in on the Yamaha. If however, as is more likely, the PC is in a different room, you can use something like an Apple Airport Express to stream from your PC to it - it has an optical digital out and that can feed the optical in on the Yamaha. At a later date, if you felt the need, you could upgrade the DAC, but to be honest I think you'd find the one in the Yamaha perfectly adequate. There are some more sophisticated options like a Squeezebox which add a display and support streaming from more media players, but they're concomitantly more expensive.
Next you need to load your CDs on your computer - you're going to want more hard disk storage if you want to get all 2,000 of those CDs on there (they could take up to 1TB in all, give or take), but it'll take a while to rip them all anyway so that can come later. There are a number of media players freely available - iTunes, Windows Media Player and Foobar to name a few. Each of these has the option to load CDs in a lossless format such as apple lossless, wma lossless or FLAC, all of which give CD-equivalent sound whilst saving up to about 50% disk space on a normal CD.
Note that Airport Express requires you to use iTunes, though you can circumvent this by for using rogueamoeba's Airfoil, which is about $25, in which case you can play your music in anything you like. I'm a big fan of iTunes though, it does what it says on the tin and have never really understood its detractors. YMMV.
Lastly, you might want to consider an Apple TV, which works in the same sort of way as airport express, but adds a modicum of local storage (which allows you to play music without your PC being on), but also adds video support and has a gorgeous 'Front Row'-style interface when you plug it into your TV.