Technically, you could write everything you want to say using only Hiragana and Katakana. The problem would only arise when you try to read Japanese. That's why you need Kanji to know Japanese. You can start by memorizing the simpler Kanji. You can search on the net for Kanji that children in Japan learn. They learn a set amount of new Kanji depending on their grade, starting from the simpler and progressing to the more difficult ones.

I study Japanese, you need to memorise both hiragana and katakana, but it is said that you only need to memorise roughly 2000 kanji to be literate and 4000 to be well spoken.