Building a first State Machine circuit - Technical Help
You should look at the 40xx CMOS series.

Wikipedia has a good list:

http://en.wikipedia.org/wiki/List_of_4000_series_integrated_circuits

You also should inform yourself what you have to consider using cmos devices in real life (what to do with open pins, additional capacitors, what means open drain, output current and so on...)

Some important considerations:


Do not leave inputs unconnected
use 100nF capacitors between the supply Inputs
check if your device is open drain and if you really want it to be
check the output current a 40xx device can drive may add a driver(transistor) if you need a higher output current


Another think is maybe implement your statemachine in a logic simulator first and when it works there design a shematic using the 40xx logic gates.

This should get you started.