If you learn how to read and write first, you'll be bound by the Korean alphabet, and will speak Korean with Chinese accent. For this reason I don't think you should learn the Korean alphabet from the beginning. If you haven't pick up all the Korean alphabet yet, it would be no problem. Don't worry. If you're going to learn Korean by some books for Korean leaners, it could be a bad idea. Some books misinform. As an example of it, we hardly say 'Chun-ma-ne-yo' as an answer in return for 'Go-map-seum-ni-da or Gam-sa-ham-ni-da'. I think it's broken Korean at least in spoken Korean. It's not strange to see it in a foreign movie or TV series with Korean subtitle though, we do not say it in daily life. If you can read Han-geul right now, improving Korean vocabulary is what you do next.
http://www.wordshowers.com/index.html, this website wil help you. It's also efficient to watch Korean dramas or movies with Korean script, you can improve Korean vocabulary, pronunciation, listening all in all. And italki has some Korean members including me ;) If you want something more, feel free to contact me. Good luck.