There are many ways your project could be accomplished. The right one for you depends on tradeoffs between the amount of money you want to spend and the amount of time you are willing to expend learning how to use the components you select. Other factors are the time and tools it will take to assemble and test the device.
A quick way would be to use a controller that programs in BASIC. One product is the BASIC stamp. There are versions than connect to a USB port for programming and have a prototype area your interface circuit.
You’ll need to describe the type of switches you want to use as inputs and the requirements of the circuit you are driving. Some larger BASIC systems have keypads and output devices built in.
The BASIC controller method is a bit pricey but would get you started quickly. A PIC controller would be a compact and inexpensive way to produce your device, especially if you’re building more than one. But, on the front end, you would have to invest a lot of time learning to program this controller. Also you would need a PIC programmer. There are several low cost programmers that connect via a USB port and the programming software is free from the Microchip website. It would be a challenging task but the reward would be a skill that will serve you well on future projects.
A more practical beginner method might be to use CMOS logic. The CD4000 series has been around for many years. You could build and test your prototypes on one of those breadboard systems where you can simply plug in the components and interconnections. It will take quite a few parts. You need to latch in the input selection, generate the timed pulses, count them, and output the signal to the world.
You can test your logic design skills with the Cedar Logic simulator freeware program. Some of their more complex gates don’t exactly model the real world parts you will use, but you will have fun learning with this program. To test its capabilities I have made an application that plays the paper - rock – scissors game. The Cedar Logic simulator can be downloaded from sourceforge.net
http://sourceforge.net/projects/cedarlogic/