I have no idea what 'Pika' means, but 'chu' means mouse from what I've heard!
Hmm... Contest, or battle... That's a toughie!
Of course, Pikachu first appeared in Pok?mon as a battler, though not a very good one... (except Ash's and a few others!) Now, Pikachu seems suited for Contests with all its 'Cool' moves.
But then again, when Pok?mon series 2 (Gold/Silver/Crystal) came out, Pikachu finally could fight with a special item called the Light Ball, which doubles Sp. Attack. In that case, Pikachu's nearly as strong as the legendaries!
Choices, choices...