There are already some really detailed replies to this question, so I'll comment on some different points... :)
Firstly, I've never made a separate effort to study Traditional Chinese characters... in fact, I'd say I even tried to avoid them! However, recently I was messaging a friend living in Taiwan. She used traditional characters, and I used simplified characters... and there was no problem. I could understand almost everything she said, despite rarely ever seeing (and certainly not studying) the traditional characters. The difference may appear daunting, but there is a strong resemblance in many cases. And when I couldn't recognize a particular character, the context (word order, surrounding characters, topic of conversation) generally lead to a "oh! That's what it means...!" After you begin to feel comfortable speaking Mandarin and reading simplified characters, exploring traditional characters won't be a problem. Of course, it may sometimes have its challenges, but with spoken Chinese and simplified characters under your belt, you'll definitely be able to overcome them. So I advise studying simple characters (as it is initially easier when learning to write) and not to worry so much about transitioning to traditional. Oh, and of course, studying just pinyin is (for me, at least) not a good option. At first, it may appear easier, but as you progress it will become a problem as it can't convey all of what the actual Chinese characters can.
Secondly, I (maybe controversially, lol) don't think that Chinese grammar needs to be given separate attention. Admittedly, my grammar is far from perfect, but I honestly believe that the grammar can be picked up naturally through conversation with native speakers. I have a friend living in Suzhou who works in Chinese (completely fluent), and she also suggested focusing primarily on building vocabulary, as the grammar can be surprisingly flexible.
Okay, that's all. Hope it's some food for thought.