>First, I've just been going through the default English translation on quran.com[1] . Is that the best version and translation to use?
It is better to rely on a translation that has at least a brief introduction and some footnotes that describe the author's word choices and interpretive framework. For example, AJ Arberry's translation flows beautifully and makes significant allusion to Judeo-Christian symbols. Muhammad Asads is probably the most sophisticated in that he always cross-references with the dominant commentaries of the Islamic tradition. I always recommend his work first because it translates the idiomatic expressions culturally and not literally. For example, how do you translate "A bird in the hand is worth two in the bush"? He translates idioms and then explains the meaning in a footnote. You can also try Abdel Haleem, although I don't rely on it much. I really recommend Muhammad Asad, because he is not only a scholar, but a Western jewish convert who lived among the Arab bedouins for a long time. He can translate cultures very well. Also, you can order a free hard copy from CAIR with beautiful calligraphy inlays, parallel transliteration and original Arabic.
>Second, what context should I keep in mind while reading it?
I recommend How to Read the Quran by Dr Carl Ernst.
> Do many people today think it should be taken word-for-word literally?
Please don't. This is how Christian fundamentalists read the Quran, not how Muslims have traditionally read the Quran. In the past, some scholars talked about reading the Quran literally, but what they meant by "literally" was not what some unlearned literalists think of today. This probably makes little to no sense, but the point is, don't read it literally.
>Is there anything else I should be reading alongside the Quran to help me better understand it?
A good biography of Muhammad perhaps. Karen Armstrong, Tariq Ramadan, Martin Lings, and many more have published great books. Dr. John Brown's Muhammad: A Very Short Introduction may be a good one to start with.
>Is it typical for Muslims to read the Quran?
Unfortunately no. Most muslims in the world do not understand Arabic. So when "millions read it in the month of Ramadan" as a comment said elsewhere, they recite it without understanding. However, compared to Christians, Jews or any other scripture-based religion, Muslims as a whole spend way more time with their scripture.
I'm around Jesuit priests all day, and I don't think even they come close to daily devotions of the average muslim layperson. I don't even consider them very devotional, but that's my opinion.