My favorite brand these days is Inov-8, which I will focus on in my next post. The price of those shoes - and brands like New Balance, The North Face, Salomon, etc. - can really add up over a multi-month trek, though, and I'm considering experimenting with cheap, no-name running shoes from K-Mart or Walmart. In fact, I'll probably buy myself a pair that seems decent (good cushioning, lightweight, highly breathable, comfortable) and start the hike in them, shipping myself my Inov-8s to a resupply point 40 to 100 miles up the trail when I'll begin climbing into the higher mountains of Southern California. At that point I will know if the cheap shoes are any good and can mail them to myself further up the trail. If $20 shoes will do the trick, then I might be able to save myself $150 or more during the hike.
ADDED LATER: I looked at shoes at both K-Mart and Walmart and was not impressed. I only found possibly one model (at K-Mart) that might be breathable enough for hiking. In general, the shoes have too much padding around the foot, which will lead to excessive sweating.
During this section, many people recommend a tougher boot with a stiffer sole and covered ankles. When postholing, or slogging through snow with a crusty top that you keep breaking through, one's ankles and shins can get bruised and cut up in trail runners. At the moment I expect to keep hiking on in a fresh pair of Inov-8 trail runners, but with gaiters covering my ankles and [partially] protecting them from harm. I'll probably have my wind pants on, too, which will protect my legs [somewhat] from abrasion. I'll be following snow reports, though, and could opt for something more protective at the last minute. Also, I will try to get out early to be walking on harder snow (I have a good traction device - the Kahtoola microspikes).