Aspartame has been well documented to give you cancer, but if you're going to drink it then you need an off-balance factor. An off-balance factor is something to help keep your corresponding weight factors in control. A low fat bagel or a cereal like Honey Nut Cheerios is probably the best way to start your morning. The latter can even lower cholesterol.
Also realize that any artificial sweetener is, at the very least, better than stevia which is just as bad as corn syrup. That aspect of it is not a problem. You'll likely want to stick with salads (go crazy with the dressing to make up for calories) since you won't get your daily metabolic rate from 0 calorie diet sodas.
It has not been 'well documented to give you cancer'. At normal doses it has no impact. It is perfectly healthy. It may mess up your relationship with sweet tastes, and the acidity of diet soda will destroy your teeth, but those are different.