Exercise wise, you would want to combine a muscle building regime (weights) with cardiovascular exercise (such as running).
"Wouldn't that (breakfast) make me even fatter"
No. Nutrition is a complex issue, and there isn't a proportional law which states that 'the more you eat, the fatter you get' etc.
Skipping breakfast in the long term will only GAIN you weight.
Skipping breakfast lowers your basal metabolic rate for the entire day, which will be highly detrimental to losing weight. Why do people lift weights and grow muscle to lose weight? Because the more muscle someone has, the higher their metabolic rates, and hence the more calories they burn per unit time, hence better fat loss results. Metabolism is very important. Also, by skipping breakfast and meals, your thyroid gland halts, and your fat burning process slows, and may even halt. Also breakfast skipping can even make you lose muscle mass due to catabolic processes (usually caused by a deficiency in glycogen or blood carbohydrates). Skipping breakfast and other meals is also detrimental to keeping a smooth insulin level throughout the day, and the negative implecations of this is enormous. Finally, skipping breakfast will tend to make you binge out later in the day on simple carbohydrates and snacks high in saturated fats, again tending you to gain weight.