The production version of the home hub is running on a Raspberry Pi 2 with 1 GB of ram. The 4 cores and extra ram is helpful to run the PostgreSQL database, but it is probably possible to run the hub on a lower specification Pi. I have employed Ethernet networking, to connect to my home network, as wi-fi has not proved sufficiently reliable in my set-up. The usual caveats about using a properly sized power supply are particularly relevant for this project, as you may be providing power for additional sensors and relays.
Build a Raspberry Pi based hub to monitor and control your home