So, your total hardware can be 2 SIPO high-current shift registers (such as the TPIC68595) and 12 relays.
Or just 12 TRIACs, which will be cheaper and smaller than 12 relays, require less power, and probably be easier to build.
The commercial units I've taken apart use TRIACs. Unfortunately they're either conformal coated such that I can't make out the part number, or they use house part numbers.
You may want to look into an ethernet shield to put your arduino directly on the network, and check out a hardware real time clock, such as the DS1307, to keep time of day.
-j