You start by writing a complete specification for the device you wish to create. Then you research all the different hardware that is available to achieve your goal. Then you consider all the different configurations and software you could use. Then you breadboard it and modify it until it meets your specifications. Then you try making changes using different components until you get it working with the least expensive components available. Then you design the circuit board and have a batch made. Then you assemble them and check that they really do meet all of your specification.
Or you pay an expert a lot of money to do it for you.
Good luck!
Is this PLC or PLD type of device/system?
If PLC, there is a 1 bit PLC IC designed by Motorola MC14500 that is still avail.
Could also refer to a programmable processor (e.g. PIC).
You can't. No matter how simple you make it, the costs to fabricate it will not be low.
If you mean "low cost" in terms of the sticker price that you can sell it at, in large volume, and still make a profit, that's a very different question.
So what does "low cost" mean to you? What kind of volume are you planning for?
You can not even specify a programmable logic device for the price at which you can purchase one. If you want to experiment, that is a place for an aduino assembly. If you are thinking of production, this is the wrong venue to ask.
Also, an EE should have enough education to understand the process.