Reading comprehension is a difficult thing to prep for. Ask 10 people and you will get 12 opinions. The most direct way to prep for CARS to practice the CARS section. Reading comprehension is important on the entire exam, especially in CARS, but ultimately the best practice is the real thing. Apparently, the CARS section is not very different from the old Verbal so there are plenty of materials out there for you to do that kind of practice. That being said, practice is better reserved for a dedicated study period where you are actively trying to "learn the test", so to speak.
In terms of improving general reading comprehension I think the best publications out there are Harper's, McSweeney's, and the Economist. NYT opinion pieces are good because they are short and very easily digestible but I don't think they are really very challenging, but the CARS section is honestly not that very challenging to comprehend, the trick is learning how to think like the test writers. Non-fiction is probably more useful to you than fiction for the CARS section since most of the material will be analytical rather than literary. In other words, you are more likely to see a section analyzing Proust than reading the man himself. Not that you shouldn't read literature anyway.
The exercise I recommend with whatever material you use is one typically learned in any introductory philosophy course:
On the first read of an essay or chapter you should be able to:
1. Identify the author's argument.
2. Identify the author's position and imagine where another might oppose her.
3. Identify where in the essay what kind and how much evidence the author employs to defend their argument.
On reflection or on second/third read you should be able to:
4. Determine the consistency of the author's argument.
5. Determine the strength and relevance of each piece of evidence the author has offered you.
6. Understand which parts of the author's argument are the strongest or weakest.
All of these 6 points translate to one or more types of questions often seen in the MCAT CARS section. Commonly seen: "What is the author's main point?", "Which statement, if true, most weakens the author's argument?", "Which of the statements from the passage most strongly supports the author's claim?", etc. etc. etc.
If you are able to identify those six basic components, and do so repeatedly, you will get better at doing it reflexively whenever you read anything and once you start practicing the real CARS section, you will reap the benefits.
I would pick three publications and follow them (for free) over the period of the year. Better yet, pick publications which are all over the political spectrum so that you can get used to digesting arguments from different authors and schools of thought (also, so you won't run out of free articles for the week so quickly) and pitting them against each other in your head. E.g., The Nation for the left, Harper's (center-left)/Economist (center-right) for the center, and The National Review for the right. All high quality, all very different from one another.
