I guess I was under the impression that the core would need to hold the actual video file captured by the media director in order to be available to the other media directors. But you are saying that I would/could have the media director encode the file to be stored, and have them available to all other media directors, which does make sense. I am confused by this because this seems like it would require the media director to have some horsepower for the encoding, but it needs to be quiet and low power. Perhaps if the encoding is done in hardware, on the capture card installed in the media director that the media director PC specs could still be fairly conservative? I want to keep the noise down near the tv. Is this how it should be done?
On the question where the encoded file is stored... this depends on what storage devices you have added to your system. In a simple system this might be a single Sata drive inside your Core (say a 500gb drive for example). But you might also have a PC booted into XP/Vista or a NAS on your network that has some storage you want to use so you would connect it to the LAN and allow your Core to detect it and then use the on-screen wizard to configure how this storage will be used. Once you have added this new storage then you can forget really where it is physically for making recordings of TV or storing a CD or DVD. All MD's on your system can then access all the recordings wherever they are stored.
On the question of the MD doing the encoding... You would be using a capture card with a hardware encoder like the PVR-150/250/350/500 etc so all the hard work is done in hardware on the card. However you are correct in saying that the MD that has that card installed will be a larger (and possibly somewhat noisier) MD than you would otherwise want. So ideally the sources you are capturing would be in a location where a slightly noisier MD that is physically somewhat larger can be accommodated. Once you have decided on the MD hardware to use then the video capture will happen on the card and then the MD will send it to whatever storage you have decided to use (wherever it is on your LAN).
We user PVR style MD's which are reasonably compact and are suitable ergonomically and aesthetically to be located say under a TV or nearby with say a Cable/Satellite box as the video source. Sometimes in small systems for say an apartment or small house this unit is often the Core as well. The limitation in this scenario is providing space for all of the TV cards and the capture card in such a slimline box. Other times the capture needs to be done in a room where you would not want to locate the Core... so in this case we would use a similar enclosure but use a slower processor and sometimes a less capable motherboard to reduce energy usage and therefore the need for cooling. This reduces fan noise obviously.
The beauty of LinuxMCE is that all these capabilities, and of course many many more, are there for you to build your system with - the challenge when first learning about the system is to understand how/when all the options/configurations should be employed.
All the best