Andrew MacAndrew's translation of the "Brothers Karamazov" (1970; the one that's been used for the past couple of decades for the Bantam paperback) is, I submit, far and away the best that has been done into English since Dostoevsky's book was published in about 1880. It reads naturally and does not contain too much slang. The most impressive translation of Dostoevsky into English I've come across is Jesse Coulson's "Crime and Punishment." It's simply astonishing, but he never did "The Brothers Karamazov."
NOTES ON OTHER TRANSLATIONS:
* The translation by Constance Garnett (many editions): Avoid it! High-toned and dense. Will make reading "The Brothers Karamazov" far more difficult than it has to be. People who are into Dostoevsky really detest this translation: it's tough going: stale and stuffy throughout. When will this thing die? I'm guessing this is the translation used for so many cheap editions (e.g., Wordsworth Classics, Dover Thrift Editions, Penguin Popular Classics, etc.) because it's public domain by this point and the publishers don't have to pay anybody.
* The Pevear and Volokhonsky version (ISBN: 0374528373). Several scholars of Dostoevsky have come out saying this is the "most faithful" translation to date, as the book's jacket does not neglect to point out. However, other equally well-respected scholars have complained that it is breezy and inaccurate.
* The David MacDuff job (Penguin, ISBN: 0140449248). Serviceable but not sparkling. Also a bit slangy. It does, however, do a great job with the footnotes.
* The Ignat Avsey effort (This is the one used by the Oxford World Classics: ISBN: 0192835092). I confess to never having negotiated this particular one, and can only warn you that it, like Garnett's above, is British English. I have it on my shelf, though. The one advantage I can see in this edition is that it, more than any of the others, has additional stuff to help you with the reading: introduction, Dostoevsky chronology, list of characters, etc. but mainly a long section of EXPLANATORY NOTES at the back, which are keyed to the text via asterisks you find as you're reading. Thus Avsey offers the best footnotes of any of these editions, although this is not one of those texts where that's gonna be a big deal.
* The David Magarshack translation. Haven't read it. Sorry.
* There is another edition I'm aware of: The translation by Louis Hechenbleikner and the Princess Alexandra Kropotkin, which first came out in 1949 and for which W. Somerset Maugham wrote the introduction. The translation has a fair reputation, but the problem is that it is so thoroughly out of print that you'd probably have to search through rare book shops to find it.
Bottom line: MacAndrew's read most swiftly and naturally for me. It's like you're not even reading something that has been translated!
(Note that Amazon's page on the MacAndrew edition The Brothers Karamazov (Bantam Classics) gives the impression, at least in declaring that the book is "by Fyodor Dostoevsky and Konstantin Mochulsky" that Konstantin Mochulski is the translator. Not the case: Mochulsky merely wrote the 10-page introduction. The translator is still Andrew MacAndrew.)