Wow thanks for all the replies! My responses below ...
What size do you want for the finished product?
Some of the small Arduino boards are so cheap it is hardly worth making a PCB unless you want a large quantity.
How will it be powered?
Answer - Small as possible. The prototype is 5 resistors and 5 LEDS
Answer: Right now just using the 5V on the Uno but could go 3V. I need to hookup some kind of power supply in the form of a battery holder ... but I don't know what would work. Suggestions?
You want to assemble it yourselves? I'd go with a thru hole design, with a separate FTDI module that would be plugged on for programming.
Here's a single sided board you can send off to iteadstudio, have multiples of 10 PCBs made up for $14.90 plus shipping.
Parts inexpensively purchased from dipmicro.com or taydaelectronics.com.
Add as many or as few LEDs as you want.
For a lower power usage board, use a 8 MHz crystal and a 3V battery pack (2 AAs or similar).
Or go with 16 MHz crystal and a 4.5V battery pack (3 AAs or similar).
Don't forget a socket in case they zap the processor.
Processor can be '328P or a '168.
I designed it as single sided for those wishing to etch their own.
After bootloading from an Uno (or Atmel AVR ISP MKii), then download new programs with an FTDI Basic or equivalent.
Can have a programming party at your house or something.
I'm such a noob that this is all greek to me, sorry. What is an FTDI module? How is it plugged in/embedded in the PCB? What is a 8MHz crystal or 16MHz crystal? What is a "socket" and where does it go to protect the processor?
I love the suggestions .. would be great to do a programming party with all the kids ... but like I said, I don't really understand much of the above. I fell like I need this explained to me like I'm 5 :)