If there are 2 people that have at the start of combat effects ( i.e Garth aqualad, and Silver Surfer). My opponent controls Garth and I control silver, who's effect goes first?

Same for at the Start of recovery effects?

Basically, the primary player places all his effects on the chain first, then followed by each other player.

The chain resolves last in, first out.

At the start of the phase triggers, the player with the initiative is the primary player.