The cheapest way overall is to buy the right components first
You will probably want a decent display, preferably VGA, quite possibly touchscreen.
You will want a motherboard that will do everything you need it to at the moment, plus a bit more for future updates.
As for power supply, you will want the one that does exactly what you want it to do, such as shut-down/start-up controller, low-voltage shutoff, voltage regulation etc.
You can go cheap, but in the end you will probably find yourself buying better parts in the end anyway, and the overall costs will be more than if you got it right first time