Can I attack both the player and a planeswalker the same turn?
Yes, after you choose which creatures are attacking, you may choose whether they are attacking the defending player or a planeswalker that player controls.

From the comprehensive rules:


  508.1. First, the active player declares attackers. This turn-based action doesn't use the stack. To declare attackers, the active player
  follows the steps below, in order. If at any point during the
  declaration of attackers, the active player is unable to comply with
  any of the steps listed below, the declaration is illegal; the game
  returns to the moment before the declaration (see rule 717, "Handling
  Illegal Actions").
  
  508.1a The active player chooses which creatures that he or she controls, if any, will attack. The chosen creatures must be untapped,
  and each one must either have haste or have been controlled by the
  active player continuously since the turn began.
  
  508.1b If the defending player controls any planeswalkers, or the game allows the active player to attack multiple other players, the active
  player announces which player or planeswalker each of the chosen
  creatures is attacking.