Hi automan.
Doing your practice UNTIMED to give yourself time to learn to understand the passages and get the questions correct will be a key aspect of your CR and RC success.
For some tips on how to practice GMAT Verbal for best results, see this post.
Three Key Practice Tips for Mastering GMAT VerbalAlso, as you suggested, doing reading outside of the GMAT can be helpful as well, although it's also powerful to go through MANY CR and RC questions. After all, you are reading as you are doing those questions.
You could read articles from the following publications to improve your reading comprehension in a variety of topics.
• Smithsonian
• BBC History
• Life Magazine
• Economist
• The New York Times
• New Yorker
• Archaeology Magazine
• Science Magazine
• Scientific American
• Science Daily
• Astronomy Magazine
• American Scientist
• Atlantic Monthly
• Physics Today
• Wall Street Journal
• Harvard Business Review
• Harvard Magazine