None. This was fifty years before he was born. Nor did he ever "join a theatre". A theatre is a building you put on plays in--you cannot join it any more than you can join a bridge or a warehouse. What Shakespeare joined was an acting company, called the Lord Chamberlain's Men, and he did it when the company formed in 1594 (he was a charter member), eighty years after the date you propose.
The Chamberlain's Men
Shakespeare belonged to an acting company.
Shakespeare only would write poems and plays for his company the "Kings Men"
He was a member of an acting company.
Shakespeare did not join a different company. The Lord Chamberlain's Men merely changed their name to the King's Men. The company remained intact.
Shakespeare co-founded the Lord Chamberlain's Men in 1594.
Shakespeare was a founding member of the Lord Chamberlain's Men in 1594, not 1596.
He didn't. He was with the King's Men when he retired in 1613.
Shakespeare helped form the Lord Chamberlain's Men in 1594. The occupied the Theatre and the Curtain playhouses until 1599 when they dismantled the Theatre and rebuilt it in another location, changing the name to the Globe.
There is speculation that Shakespeare acted for Pembroke's Men or Strange's Men, but there is not hard evidence of it. In 1594 he helped found the Lord Chamberlain's Men.
The Chamberlain's Men
Shakespeare belonged to an acting company.
Shakespeare only would write poems and plays for his company the "Kings Men"
He was a member of an acting company.
The exact date is, sadly, unknown. Some time between 1585 when the twins were born and 1592 when Greene lampooned Shakespeare and paraphrased a line from one of Shakespeare's plays, Shakespeare moved to London and became an actor and playwright, working with one or more companies in one or both capacities.
Shakespeare did not join a different company. The Lord Chamberlain's Men merely changed their name to the King's Men. The company remained intact.
The Lord Chamberlain's Men was formed in 1594 and Shakespeare was one of its charter members, so he didn't actually join it. He had by that time already written a few plays and was an actor. Later, under King James I, the Lord Chamberlain's men changed their name to the King's Men. This company did not own the Globe Theatre or any theatre; that was a different group of partners, one of whom was also Shakespeare.