To begin with, there isn't any difference between "except" and "except for" in terms of meaning. However, depending on syntactic context, one may use both or only one of them. The following examples will hopefully illustrate this.
An exception goes against the rule, it contradicts the rule. It usually marks an outlier as in: "Everyone in our group could speak Japanese except (for) me."
Other times, it marks something that contradicts an assumption, like: "She did a great job. All the walls in the house were freshly and neatly painted in pink... except that I do not like pink." She generally speaking did a great job, but she missed to check in with me about the color. That last fact contradicts the statement that she did everything well.
"Besides" also marks an outlier, something separate from a group, rule, or assumption, but it does not usually contradict the rule or opposes the group. For example: "I have nothing against adopting these two guinea pigs. Besides, they are so cute!" The fact they are so cute was not considered or thought of initially, and instead of contradicting the previous statement, it actually supports it: yet one more reason to adopt those guinea pigs.