This actually depends on what your reason is for learning Japanese.
I agree with the other replies about hiragana, katakana and the first 100/200 kanji being essential to your learning.
If you want to go study for the JLPT, or if you want to translate at some point, then it would be best to start with reading and writing first.
If you are not planning on using Japanese much when it comes to reading or writing, then it could be better to focus on listening and speaking first.
Personally, I would recommend doing all of it, even if you mainly focus on one or two aspects. For example, if you choose to focus on speaking and listening, you can also learn some extra kanji from time to time. Or if you learn to read and write, it could be very useful to study vocabulary as well as having some listening practice.
However, I would recommend not to neglect any of the aspects completely.