Building my first desktop computer, Part 1: Choosing the parts

So my current computer, a Dell Studio XPS 8100, is starting to show its age. Apart from not natively supporting USB 3.0, I am also getting random errors I cannot reliably reproduce. With eBay's 20% off sale on computer parts, I think I found the best time in the foreseeable future to upgrade, as well as learn how to build my own computer. As a highly proficient computer user, that learning experience was bound to arrive sooner or later.

The use case
This computer will be used for midrange computer gaming, so it will need to, at a minimum, be able to handle graphics for moderately demanding games, as well as those I may want to play in the future, including World of Warcraft, Fallout 4 and Borderlands 2. Otherwise, I may also need to burn the occasional Blu-Ray disc, watch the occasional Blu-Ray film and transcode the occasional video. Of course, a computer that meets these requirements will be more than enough for web browsing and emails.