"I shall ___" means "I will ___". But "I shall" sounds very formal. Most people only use "I shall ___" in a few specific situations:

• When making a promise during some kind of ceremony, like in a wedding.
• When speaking poetically. Here is a line from the play Hamlet by William Shakespeare, as an example:

  He was a man, take him for all in all, I shall not look upon his like again.

• In a political speech.
• On TV shows and movies, superheroes and villains sometimes use "shall":

  No matter the odds, no matter who tries to stop me, I shall prevail.

The speaker in the example above is using "shall" in a joking way, to pretend that he is like a superhero for fighting against the spider.

In most cases, use "I will ___" to announce things that you're going to do. Use "I'm going to ___" to talk about things that you've already planned to do.