You still choose which player or planeswalker Zurgo Helmsmasher attacks.

If Zurgo enters the battlefield before the combat phase, it will attack that turn if able. If it enters the battlefield after combat, it won't attack that turn and will usually be available to block on the following turn.

If, during your declare attackers step, Zurgo is tapped or is affected by a spell or ability that says it can't attack, then it doesn't attack. If there's a cost associated with having Zurgo attack, you aren't forced to pay that cost, so it doesn't have to attack in that case either.

Each time a creature dies, check whether Zurgo had dealt any damage to it at any time during that turn. If so, Zurgo's ability will trigger. It doesn't matter who controlled the creature or whose graveyard it went to.