First you need to decide how big your initial system will be. Are you talking about one room only, multiple rooms? The linuxMCE system includes systems for lighting, HVAC, telephony, and security so for now we won't worry about that. We will just focus on the first part of the system, the CORE.
If your only planning on a single room, and a single computer for now, The Hybrid Core install will be what you want. The hybrid system has the CORE and Media Director both on one system, and is the default install for LinuxMCE.
If you have a larger system in mind, and want a dedicated CORE system with individual Media Directors for each room, You want the Basic Core Install.