a shield is something you place on top of an arduino to enhance its functionality (XBee, Ethernet, Motor control, etc...)
Yes, you can make a stand alone board with an arduino chip. that is no problem, all you'd need is a crystal and a few capacitors and power supply. Look for breadboard arduino and you'll get plenty of hits on how to do this.
Regarding the power supply, 7805 with 24V at its input will fry the thing. There are some several chips that you can cascade (to share the power dissipation) or use with a power transistor to regulate that sort of power, but it will always end up regulating by dissipating. If you are serious about the projetc, I think a switched power supply on your board would be better.
The UNO has a sketch that will transform it into a chip programmer. You can then program any chip in the AVR range. You do however, need a bit more knowledge about fuses (not the ones to limit current), AVR-GCC and makefiles (although some of these chips have been adapted to the Arduino IDE). But there are plenty of resources on the internet.
Look for ATmega48 or ATtiny along with Arduino to see what people have been doing.
Some of the times, the problem is not so much the inputs and outputs, but the memory of the chip. Hence a smaller chip, may or may not suit your project.
One interesting board that resembles a lot like a PLC is this one: http://ruggedcircuits.com/html/ruggeduino.html