Here is a free program for designing circuit layouts.
You can buy single sided 4" x 6" copper pc boards for
$1.95 each at PartsExpress Here <=-
I would recommend a simple led strip for your first board.
All you need as far as the components are concerned is a male 4 pin molex adapter, leds, and resistors. You will also obviously need a soldering iron, and solder.
You can print any design in black on matte paper or staples basic photo gloss paper with a laser printer if you dont have one goto Kinkos or similar and be sure to print at max DPI or set it to transparency if that option is available.
You can have your name, or logo, of your project etched in copper on your pcb.