http://www.goarch.org/chapel/I have an email subscription to daily readings from our Church (available at the above link). I find it helpful because the readings are usually fairly short (with a few exceptions), and they also have some info on the Saint(s) of the day usually.
I find that hearing about the Saint of the day is helpful, because these are the people who put the Word into action.
Even if the reader doesn't "believe in Saints," as such, reading of Missionaries & Martyrs who served God and gave their all can keep the focus off of the what-does-the-writer-mean-by-the-use-of-the-definite-article-here type of focus.
I think the most important thing is to focus on faithfulness in small things, and focus on & apply what parts of the reading we DO understand, instead of trying to do something "big"
(sometimes being analytical is a matter of looking for loopholes - if we hold our own feet to the fire on the parts we DO understand, that can help with that part.)