Great question (and suggestions)!
My wife and I begin our day with a time of reading and prayer. Our method is quite simple: I read it aloud and she follows along. It's a long-term commitment to read the entire Bible through; so, we make sure to always follow through (even when we are traveling).
The first time that we read it, we followed a mostly linear path through the New Testament and then Old Testament before returning to the New Testament again. Now, we are reading it simply cover-to-cover (from Genesis to Revelation).
We often consult other passages or chapters too. For instance, we recently read the story in I Samuel about the Ziphites betraying David's whereabouts to King Saul. From memory, I understood that this corresponds to Psalm 54. So, we read that passage too.
We also have read a different translation for each of our trips through the Bible. I also make sure to have source texts available (via my iPad, phone or computer) to consult too. This is especially helpful when pondering how a passage is phrased.
I must say that this is my favorite part of each and every day! Not only does this strengthen our knowledge and understanding of Scripture, but we also grow closer by studying the Word together. I personally feel that there is something powerful about reading (or hearing) the Word of God aloud.
I know that many people read through the Word of God in different ways. I must admit that I am now somewhat partial to the order of traditional canon. I also believe that a strong familiarity with the Old Testament is vital when it comes to better understanding the New Testament (and vice versa). A good grasp of the Law is very helpful with the Epistles that reference passages from the Law too.
I suppose that the best method is the one that we stick with. When I first believed, I read through the New Testament and then the Old Testament and returned back to the New Testament and read through it again. As a new believer, this helped me immensely. So, when my wife and I began reading together, we followed this (and she remarked how helpful it was to do it that way).
Interestingly, we've discovered that it doesn't take quite as long as a year now with each journey through the Word. We're not rushing through it either. We also still study independently from our readings together too.