Arduino Vs DIY board
Pre-built board is more likely to work out-of-the box.  Making a DIY breadboard will give you more insight.

I would do both things: buy a professionally built Arduino, buy the components to make a breadboard clone.  While you clone, you can use the professionally built Arduino as a reference, which you know that it works.

Read a lot.  Over time, more things will start making sense.  Don't hesitate to read the ATMega datasheet (at least skim through it), and other Atmel papers.

Here's a page on the Arduino web site, which describes how to use Arduino as an in-system programmer.