Japanese actually uses all three alphabets, and you'll be learning all three. Although hiragana and katakana can be memorized quickly, kanji is usually learned gradually because the kanji system is quite extensive (as in, over two thousand characters... yikes).
Hiragana (ひらがな): The basic alphabet. This is used for particles, verb conjugations, etc.
Katakana (カタカナ): This is used for loan words. For example, cake did not originate in Japan. Because 'cake' is a foreign word, it is written in katakana (ケーキ).
Kanji (漢字): Chinese characters. These are used to write stems of verbs, adjectives, and adverbs, and also to write words. Kanji and Hiragana are usually used together.
For example...
"Kore wa watashi no orenji desu." --> "This is my orange."
If written in all hiragana, this would be
これ は わたし の おれんじ です。
But, "orange" is a loan word from English and so is written in Katakana.
これ は わたし の [オレンジ] です。
The Kanji character for "I", or "Watashi", is 私. Sometimes, if the character is too difficult, the word is left in hiragana. But most times Kanji characters are used whenever possible.
これ は [私] の オレンジ です。
You can see how all three alphabets can be used in a single sentence, which is why all three alphabets are quite important. D: