Actuall you should learn both and Kanji as well.
Katakana is ofen used when writing foreigner's names or foreign words, and in daily use Hiragana and Kanji are used.^^/
As for "Happy New Year",
It would be "新年おめでとうございます." in Japanese.
新年(しんねん) is Kanji, "おめでとうございます" is Hiragana.
Also you can say, "ハッピーニューイヤー" for that in Katakana.
(Happy = ハッピー/ New = ニュー/ Year = イヤー)