These are some general guidelines for starting to study Japanese.
First, learn the basic pronunciation of Japanese sounds. If you don't learn proper pronunciation first, you will have to unlearn many words you learned incorrectly later.
Next, learn the hiragana and katakana. The sooner you learn how to read the basic scripts of Japanese the better. Relying on romaji will make it more difficult later on. Also, learning these will open a wide range of possibilities for language study resources. Katakana is especially useful for people who are moving to Japan. The reason for this is that many of the katakana words you will encounter in Japan are based on English. (Exp. miruku = milk) It therefore usually requires very little effort to read it. Since it is sharper looking than any of the other scripts it is easy to pick out katakana words on packages. This is incredibly helpful for shopping and reading menus.
What words should I learn?
The best thing to do is to learn words that you will use often or that you will hear often. For instance, if you have a cat then most likely it will come up in conversation at some point, so it would be wise to learn the word cat. However, if you don't talk about the North Pole all that often, don't memorize that word just to increase the size of your vocabulary. Those kinds of words will come later. Time is much better spent memorizing useful everyday vocabulary.
How do I set up my computer to read Japanese characters?
Check out the Computer Setup page.