Do both at the same time! But if I had to pick, I would pick learning to speak first. Reading words and speaking them out loud would give you practice on spelling, pronunciation, grammar, and sentence structure, which would all help later on when you learn to write. But overall, it really depends on your style of learning, like Cory said. Just learn it in a way you're most comfortable with :)

It depends on the language, how you learn, whether you will be around native speakers and how you'll be studying. Though I have a good ear and can repeat what I hear accurately, I don't learn from my ears. In order for me to learn the word, I need to know how to write it. But writing it doesn't do any good for spoken language unless I know how to pronounce it. Since my goals are to be able to speak language I need to learn both. I want to learn to read and write as well, which will help me when I travel, so the need to know how to spell words to learn them is not a burden.

This subject is frequently debated- personally I find it is best to force yourself to speak the language as soon as possible. Read a lot and speak a lot, then writing comes pretty easily.

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