Great first step (learning the alphabet)! It's good to learn how to read and pronounce a language right off the bat. Or else how can you do much else? The next step is to just learn! Work on grammar, vocabulary, listening, reading, writing, speaking, pronunciation, conversation, and culture! Haha :) Here's my opinion on language and Korean studies: http://www.italki.com/question/301202 There's nothing wrong with learning some specialized or technical vocabulary (though I'd save the bulk of it for a little further on - low-intermediate and up). If it's something you're interested in, you need to know how to talk about it. Whether it's computer, math, engineering, etc specific vocabulary, it's great to be able to discuss your interests with someone. One day you'll run across a Korean with the same interest too, I'm sure, and knowing a decent number of related vocabulary will be extra helpful for delving in and explaining what you do/like to do. You don't want to start off with something too grammatically complex. You wouldn't give a 3- or 4- year old a sentence about rocket science, eh? Rocket science, physics, engineering, etc would be far too complex for children to start out with. Master the pieces and learn to put them together. You want to build a strong foundation. Just remember that you're not exactly a little kid. Feel free to push yourself outside of your comfort zone gradually to make better, stronger, longer sentences. Korean relies a lot more on grammar than vocabulary to convey certain meanings and nuances, so take it easy and don't stress. Good luck and feel free to contact me for more help and/or resources :)

MY IDEAS ON STUDYING VOCABULARY: http://www.italki.com/discussion/91279 Learn vocabulary in Korean, just as you learned vocabulary in English - through need and use. When you read or listen to something, look up what you don't know. Use those words in your own writing and speech. Pay attention in the future to see if the word comes up again. When you write something or speak, look up what you don't know. Continue to use those words and to watch and listen for them. Study vocabulary in multiple contexts, not as isolated words. It's like if people only spoke one or two words at a time to you when you were growing up. You'd have quite a difficult time trying to make natural sentences or use those words yourself in other ways. Your English would have ended up very...poor. As an added reinforcement - not as a sole way to learn, but as a way to review and test yourself - try using flashcard systems, word lists, etc. Working on vocabulary will help with 한글 too.

You can learn the grammar and basic vocabulary. Or conversational sentences.