The Qur'an suffers from the same translation problems as the Bible, only more so: impossibility of conveying beauty of original language, cultural differences between time and place of writing and reading, human limitations of translators. While the Bible is now typically translated by committees, the Qur'anic translations available in English are by individuals, often not native English speakers, coming from quite different Muslim populations in south Asia, Indonesia, Iran, Turkey, Arabia. All this just to remind you that, just as any serious Bible reader would look at multiple translations, so should anyone trying to give the Qur'an a fair chance in English. I wish a parallel Qur'an existed like the parallel Bibles you can buy!
Having expended a fair amount of time and money buying most of the translations and poring through them, I'd list four worth your consideration. (1) Start with a straight reading copy in straight English: M.A.S. Abdel Haleem. The English is natural, the text is single-column without the Arabic on the right. But there are no notes, and even if you understand the words, the sentences make little sense to a non-Arabic non-7th-century reader without some explanation.
The notes, though, are where opinion starts to creep in from the various Muslim viewpoints around the world. I ended up with three more options: (2) Abdullah Yusuf Ali. The main text itself is almost unintelligible, because he had a misguided notion of conveying the beauty of classical Arabic with a kind of ersatz King James Version scrambled by Indian English, and you probably don't even understand the KJV of the Bible as well as you think. In this edition, the copious notes offer sometimes the historical background, sometimes a deeper analysis of the original Arabic, sometimes a pious kind of "Life Application." They are pretty good in a non-scholarly way and as a non-Muslim thoughtful reader, if I had to stick with one set of notes I'd go with these.
But if you want to read as if had grown up in a normal Muslim background, that is, to know the traditional interpretations and views of major commentators contained in the hadith, add (3) Muhammad Muhsin Khan and Muhammed Taqi-ud-Din Al-Hilali. Their notes quote chapter and verse verbatim from the most historically important commentators, Tabari, Qurtubi, and Ibn Kathir. But this doesn't really work as your main translation. Though the text itself is a lot better than Abdullah Yusuf Ali's, it wanders through a maze of parentheses and untranslated Arabic words. And there are not enough notes: you don't get "this came up when Muhammed was asked about the inheritance of women,'' or "compare with surah x: y."
That brings you to (4) Muhammad Asad, an Austrian convert, born Leopold Weiss. His translation itself is about on a par with (3): it more or less works in English, but you may get distracted by all the parentheses and there is a little too much flowery language. His notes are at least as numerous as in (2), but Asad/Weiss naturally had a better idea about what might confuse the average non-Muslim reader. He offers a reasonable combination of the scholar's hadith and the layman's history plus moral application. Unfortunately, the hadith are not identified with the name of their authors, the opinions of Asad himself are frequently seen by the Muslim mainstream as non-standard (read: incorrect), and you can't tell the difference. You don't know whether what any given note says is just Asad's individual, controversial opinion, or a point of view most Muslims are at least familiar with. What's more, this is a huge book, like volume M of the Encylopedia Britannica. You're not going to be carrying it to class or reading it in bed. That said, it is the only one of the four that gives a transliteration of the Arabic so that the Muslim convert can read it aloud without knowing Arabic.
You probably don't want to spend all this time, money, and shelf space, so I'd say: read (1) the Abdel Haleem translation and with (2) Abdullah Yusuf Ali's notes to hand. And lobby the next smart Muslim you meet to give us a reasonable all-in-one Study Qur'an!