PCBcart[dot]c*m cheap and reliable chinese service!
As for design: Cut you teeth with Express PCB (free dowload with schematic software included), see how you get on! The schematic software is worth having anyway.
I porgressd for there to Sprint PCB (about 40EUR) which is really easy to use and include some great tools.
RS components in the UK have launched Design Spark, do you have RS where you are? It's a very professional package and has no pin count limits (unlike Eagle, which is now part of the Farnell group). But it is MASSIVE and takes some getting used to! The libraries are built from RS stock, not just generic parts so BOM generation is really simple. Me personally i would rather just lay out a dip16 package and label the pins than serch through every opamp RS have. But it's free, but more of a professional option i would say!