Losing weight is more about what you eat than how much you exercise. Working out helps out with fitness and health (mental and physical) but can seldom over come a poor diet.
I completely agree with your last sentence here. If you combine the two, its a great formula toward better health and weight loss. Nutrition was the critical component that helped me drop 25lbs so far this year (starting in mid December 2013). I would kill myself at the gym, yet ate like crap and never could drop much weight. Several times burning out or getting frustrated because the number would never move. Then started working with a trainer who coached me into understanding how the two things work together, helped me look at veggies differently and stressed the importance of "the journey of health over the destination". What a difference it made for me.
Your goals are reasonable and will add up. Discipline is your friend but don't forget to live. Hang tight, have a solid support system. You'll get there, no worries!