It barely matters what you eat as long as the total calories are sane and you're lifting as heavy as you can. The problems with processed foods are two-fold: primarily it's that they're dense with calorie content so you get a lot of calories for not a lot of food. The other problem, and it's not really one if you get it elsewhere, is that they're pretty much all low on protein.
The hardest part of getting your diet right is making sure you're getting enough protein. A lot of food faves have a lot of carbohydrate content in comparison to protein. Getting the same amount of calories from carb and protein, or 40% protein and 30% carb can be tough. Fat's easy, because it's 9 calories a gram instead of 4.
tl; dr - I get steady weight loss of 1 lb. a week, even having pizza once a week for the last six months. Half a pizza, 1,000 calories. I eat it on a gym day, though. I'm trying to get down to 10-12% body fat and probably have about 2-3 months to go, so I may hit a wall, but in my experience, a little bread ain't the devil.