Future simple: instant/immediate decisions, promises, offers, predictions, suggestions, future facts (e.g. I'll be home all afternoon"). You can also use "shall", for example, to suggest something ("Shall we eat out tonight?"). If you want to offer or suggest something using pronouns "I" or "we", you use "shall" instead of "will".
Be going to: future plans and intentions, predictions based on evidence.
Present continuous: future arrangements.
You can often use either "be going to" and "present continuous" interchangeably.