English, like all living languages, is complex and constantly-changing; what is acceptable in spoken English is not always accepted in Standard (written) English. The key to improving your English reading, processing, and writing skills for the GMAT is consistent high-quality practice. It's true that native speakers have a big advantage -- they have typically been listening to correct English for at least two decades. Non-native speakers, however, have a small advantage -- they (unlike native speakers) have not been listening to incorrect English for two decades. Build your study around quality writing and daily practice -- and start as early as you can.
A note about The Economist in particular: you may be tempted to choose that above all the others, as it is the most business- and world news-focused. I believe doing so would be a mistake! The Economist is known for its very precise and concise use of language; you all should be reading it for this reason. On the other hand, The Economist assumes a very high level of familiarity and comfort with not only standard language usage, but also the rarer, more complex, and more concise usage of English found more commonly in the humanities (it also occasionally chooses British English usage over American English usage). The other three periodicals mentioned above have a smaller portion of their content devoted to finance and business and a greater portion devoted to the humanities -- often without The Economist's trademark concision. You will get more practice tracking longer English sentences, which can also shed more light on English usage: sometimes things are easier to understand when more words are used to explain! In addition, the greater variety present in the other periodicals prepares you better for the variety of topics you'll get in GMAT Reading Comprehension passages. In short: use The Economist, but not only The Economist.
One Year Away From Test Day
• One half hour per day reading (or even listening to) quality English writing. Podcasts/audio books are an acceptable occasional substitute; reading words on the page is better, but only one of the two is legal or smart while you're driving to work
• Look up words you don't know, every time.
Six Months From Test Day
The above, plus:
• Take a full-length practice test to assess your weaknesses; take two more in the next two months
• Take inventory of the places you are likely to be caught due to language differences
• Start writing down idioms that give you trouble; take note of movie/book/song titles, or other key phrases in English that can help you remember the idioms
• Begin a weekly commitment to GMAT study, starting with the Official Guide. Move to other sources when you have exhausted the Official Guide material
Three Months From the Week of Your Test
• Begin taking at least two full-length practice tests every three weeks; you are taking full-length tests because the Quantitative section is also written in English. The goal is to improve your comfort level with the overall timing of the test, and to help you adjust to the range of English that appears on the full test
• One half hour per day of Grockit GMAT Verbal Study minimum; do not save it all for one weekend afternoon
• For harder CR and RC passages, you can also use LSAT prep materials
• Keep reading!
One Month From the Week of Your Test
• Take one full-length practice test per week
• Study every day, even if it's just 15 minutes. You gain much more from repetition than you do from cramming
• Keep reading!