Sigma 50-500 is a popular budget choice, many users rave about is quality and versitility. At 500mm a very steady hand is required or a great tripod. I perfer to use stabilised lenses (Canon IS).
DG is a anti-reflective coating to minimise reflection from a digital sensor to the rear lens element. In my experience this may occur only 1% of the time and in a widelife setting less than that!
For DOF, please read the following link, an excellent piece one of a series writted by Yelvertoft. The other three in the series a well worth a read.
http://www.worldphotographyforum.com...read.php?t=414