It's poorly organized, but I'm not really sure the best way to organize it, so, in no particular order...
For your music (IE, no internet radio or anything): internet or disc -> local storage -> playback software -> digital output (transport) -> DAC -> amp -> speakers. Using digital in to a receiver, it handles the DAC and amp parts.
Playback: central receiver to...whatever. A living room with vaulted ceilings will probably need some care in speaker selection, but that's its own can of worms, and not one I'm well versed in.
Input to receiver for audio: HDMI (video), S/PDIF, TOSLink (optical S/PDIF), or analog input. HDMI can carry video and audio, but how well it will work may depend on other details. Distance increases the risk of audible ground loops, and the carrying cables causing other interference, as well, so it's helpful to have the player right there.
A dedicated box, that is small, unobtrusive, and quiet, and also increases WAF, hence a very small form factor computer hidden away, or an HTPC in a suitable case. If you don't use customized software made for a remote, or use cells/tablets, there are numerous wireless controllers available, in all sorts of form factors.
Input to receiver for video: these days, mostly HDMI.
To get from audio files, or internet streams, to the receiver: some computer.
To turn CDs, DVDs, or whatever else into files: some computer (maybe the same, maybe different). For CDs, the drive (mainly its controller) matters. You can use EAC to check out a drive in a prebuilt PC. It may be in the AccurateRip DB. While notebook drives tend to rip slower, if it's got a Mediatek chipset, it should be a decent CD ripper, and will likely have a +6 sample offset.
To store files to play: some computer (maybe the same as one of the above, maybe its own).
NAS = Network Attached Storage. File shares. A Windows desktop can be a NAS just as well as a Windows server, a linux server, or a turnkey box with hotswap drive bays (99% chance it will be a Linux box, inside). The dedicated box saves you setup time, and gives you an indicator and hotswap bay for a bad drive, should you need to replace one.
A NAS is not necessary, but common to use and quite handy. The transport/DAC could be on the same PC that does everything else, or they could be split up. Usually, they are split up, so that one PC can be right next to the receiver, preferably also on the same power strip, to do the playing back. It used to be one might get a Squeezebox for such duty, but between Logitech deprecating them, and whole PCs getting fairly cheap, why not have something more versatile?
Since ripping discs chews up a good bit of time, you'll want to make sure your library is backed up. I've already had to deal with a library not backed up before, and it's tedious to treat discs as the primary backup. Er, and HDDs are cheap for storing CDs, and not bad for DVDs (BD can eat up some space, though).
If digital input works fine, a PC's included audio will be plenty, if it has digital output. If not, add-on sound cards usually have coax or optical, if not both. Analog out from a PC may work, but don't be surprised if it's noisy on its own, carries PC noises with it (basic tests you see done showing good SNR and THD aren't the whole story), or gives you a ground loop. USB audio devices typically have their own local switching PSU, and are out of the PC itself, so are typically better options for analog (today, if buying a new receiver, though, I'd try not to use analog in).
If you have any familiarity with Linux, or an interest, The Raspberry Pi 2 B+ can be made up for about $60-70, case and Wifi included, so long as some other computer stores the audio files (big SD cards are expensive, after all). If support is there yet, or coming very soon, for the relevant distros, the 2 has a much faster CPU. While you often have to deal with a little Linux and Samba to get going with networked files, RuneAudio and Volume.io have a bunch of features, tweaked UIs, so you can relatively easily remote control them, built in UIs for streaming internet radio, Spotify, etc.. They lack video, though. OpenElec seems to work well for that, but music-wise, is sort of clunky.
For getting started, you could just use a PC, with Foobar2000 to play files back with.
Finally, with DLNA support, you can have the receiver just play back arbitrary conforming streams, and there is software out there to use as a DLNA server. That will allow playback to be completely networked, yet still offer versatile computer-based control. I'm on old stuff that isn't dead yet, so I don't have any experience making use of it, myself, and am not sure how easy it is to actually set up and manage, in practice.
