I admit that I have never used 'Integrated Chinese', so I do not know how useful it is. However, FSI Chinese is IMHO outdated. If it has not been updated in the last 10 years, I would not rely on it. I know it's public domain, free and it comes with plenty of audio material, etc. but it was made ages ago, and language & society has changed in China so much. I used a German text book back a few years ago to learn Chinese, which was originally published in the early/mid 90's and fellow Chinese students used to laugh about some of the expressions, because they are not used anymore. Occasionally you can use FSI's audio material to practice your hearing comprehension, but if you have something more up-to-date, use the latter one.
If the material in 'Integrated Chinese' is divided into fair amount of lessons, that you can cover within a few days (assuming you learn 1 or 2 hour every day), that's just fine, stick with the curriculum of the book, explore any supplementary material in the back of the book, if there is any (e.g. list of words, characters, table of radicals or pinyin syllables), to make the most out of it.
It's a good way actually to begin with the pinyin syllables and to learn what sounds the initials (b-, q-, t- etc.) and finals (-eng, -iang, ou, etc.) represent. As you write, you are already familiar with the pronunciation basics, so it shouldn't be an issue for you.
The next thing I would do is to start with a lesson in the text book and first take a look at all the items in the vocabulary list, make sure you understand them, you do not immediately need to learn them by heart, after having read the reader and done the exercises you will have no problem with them, most text books come with a number of exercises that will reinforce the lesson's core vocabulary and will also repeat the vocab of past lessons. Occasionally, as you make progress and cover new lessons, you can brush up the vocabulary and grammar structures of earlier lessons, it is always a good idea to repeat, because the more you encounter with things, the more familiar you are with them.
Practicing speaking would require someone to have conversations with, so find someone who has the time to do this. If you don't have, you can still find a way to exercises yourself, though it's a bit boring. I used Audacity to practice my pronunciation skills. I would load and mp3 file that came with my text book and select a few syllables of speech (you can see waves of the audio visualized in Audacity) and listen to them again and again, trying to make my pronunciation and intonation exactly like the speaker. I used to record myself and listen to it, to check how authentic (or actually bad) my Chinese sounded. It wasn't really exciting but I discovered many of the phonetic aspects of Chinese this way. In case if you have someone to chat with you in Chinese and can help you build experience, you don't need Audacity, it's just an idea for those who really have to learn on their own.
As for listening, reading and writing, actually if your text book is good enough, you don't really have to make thoughts about them, just work on the curriculum and do all the exercises. If your vocabulary is still not that comprehensive, it is hard to find audio material other than text book audio, because most of the radio plays, TV shows, movies require you to have at least intermediary level to be able to follow the dialogs. Actually learning materials commercially available are quite good and plenty these days, so if you have time and money you could invest in some other material than your text book. As soon as your vocab gets better, you could starting hunting for some real life audio, I used a course designed for Chinese people who wish to improve their Putonhua. Actually you can just search for 普通话 as a keyword and you will find plenty of audio to listen to. Baidu's audio search is not so user-friendly and I doubt that everything uploaded here is public domain, but as long as you download it for personally use only, you don't need to make thoughts about copyright law. To this Putonghua course you will find the texts on several sites online. I need to search through my old bookmarks in order to find a link to post here.
Another interesting resource I used to practice hearing was a Taiwanese radio (教育之声） show about Chinese literature/culture, their pronunciation is a bit odd to me, but it's still OK.
I need to warn you to only start listening to these when you already have the core vocabulary, otherwise it's just a waste of time.
Writing: buy plenty of paper and good lead pencils to practice. The best paper is that has some lines on it to provide you some orientation, you can buy and print paper specially designed for exercising writing Chinese characters (boxes with diagonals or just boxes without diagonals) that Chinese school children also use to write their home assignments. If you can buy these, use them. If they are not available, use any kind of paper. Do not try to use pens, especially ball point pens, since many of those require you to push them onto the surface of the paper in order to mark the paper with ink. That's not particularly helpful for someone to who is about to learn the basic strokes (撇，横, etc.) to get these look beautifully, these will require you to have something that doesn't need to be pushed that hard, a soft graphite pencil, ideally.
If you can buy character practicing sheets (which come with characters pre-printed in light gray), buy them, they are very useful. Just make sure you know the stroke order. That's quite important. Your textbook should cover this, hopefully.