Hi, Ben, and welcome to Liberty Classroom! There are no absolutely required or essential readings for the Western Civilization courses. The bibliography that accompanies each lecture is for those who wish to dig deeper into that particular lecture’s topic.
If you are looking for a general Western Civ survey textbook that will flesh out the lecture material, I find Jackson Spielvogel’s the least objectionable of the mainstream texts out there: http://www.amazon.com/gp/product/0495913243/ref=as_li_qf_sp_asin_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0495913243&linkCode=as2&tag=thewesttrad-20
Yes, it is pricey (not excessively so, as college textbooks go), but I’m sure you can find used copies for a more palatable price.
And I hope you find the blog enjoyable!