Reddit mentions of Integrated Chinese Level 1/Part 1 Textbook: Simplified Characters (Chinese Edition)

I would recommend this textbook and to get the workbook with it. We use it at my university but I think it is more than clear enough to be used as a self study aid. As you finish the book, move on to the next level and so on. It has dialogues, vocabulary, and grammar written in a clear, concise style.

Recommended Textbooks
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Integrated Chinese - This is used in many university classes in the US. The companion CD is definitely recommended. The workbook wont be much use if you don't have someone to check your answers, as the company is pretty strict about not letting out the answer keys.

New Practical Chinese Reader - This is a great alternative to Integrated Chinese. There are also PDFs and mp3s of all materials floating around on the internet if you look.

Character Practice
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Skritter - Seriously awesome. It does have a monthly subscription though.

Oral Practice
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Pimsleur, Assimil, or the FSI course (free). I've only used Pimselur, but I've heard good things about the others. These are good for practicing your tones.

Online Resources
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Chinese-forums

nciku - A Chinese - English dictionary. You can draw out unknown characters, which can be much easier than going by radical like in other dictionaries.

You should also set up Windows (or whatever OS you use) to be able to type in Chinese (usually through pinyin).

Once you're good enough, you can find easy books called "Graded Chinese Readers" that often have a companion CD to help with pronunciation. They're pretty cheap as well if you import them from China.

Good luck, Mandarin is a difficult language, but it's also really fun. It might take a long time to see progress (I still can't read newspapers), but as long as you keep at it you'll probably be happy with your results.