You mentioned the NM draw, which means you will apply by a region or collection of units. If you draw, you will be assigned to a "ranch only". This means you will have unlimited access to the ranch, but NOT the unit or region. Some ranches are larger than others and will have more "draw" hunters than others. In NM, Ranch owners get private tag permits, which means you will have competition with private tags. Private tags are often bought up by guides who feel the ranch is their domain. Read the proclamation closely as many changes have been implemented for the 2011-2012 year. As for a region to choose, they are all fairly good and your chances of success depend upon the rach you draw and the survival rate of the goats through the winter. Last winter, we had a harsh winter and the heards looked pathetic in the spring, summer was exceptionally dry, but my experience in August was a great goat taken within 10 minutes and we spotted several shooters the day before the hunt. Scouting the ranch and good optics are a must. Good luck with the draw!
