Hello!
I am a Christian, but I have read the qu'ran many, many times.
First off, it is good to read the Bible first. I actually read the qu'ran BEFORE I read the Bible(or before I was Christian for that matter.) The reason.. Because the qu'ran is a small book.. 20% smaller then the New Testament!
So, I first read it... And there were many strange things in there that I had no clue about. Like "And remember the inflictions on Job." So I hear that something happened to Job.. But what happened!! So then I search all over, and find no answers in the qu'ran.
Later on, I read the bible, and found all what Job was about..
It is an islamic belief that the Bible is corrupted. However, I think that once I read the Bible, I got a much better understanding of what the author of the qu'ran was trying to say. The Bible is a LOT more descriptive and a lot more detailed, and so it helps to see what the Bible says to fill in the pieces.
So, since you are Christian, you have probably read the Bible. So that is good.
However, there are still many confusing things.. Like different people being mentioned, or this or that. So, it is good to read tafsir. You can find it on the computer. Tafsir ibn kathir is the most popular. It sort of mixes different details together. It answers a lot of questions about why this or that surah was "revelaed" as well as more on the meaning, etc. You can view tafsir ibn kathir online.. Just google it, and go to the first result. So yeah, that always helps.
And, lastly just read all the 6 authentic sunni hadiths. Those answer some questions here and there. And, ibn ishaqs biography of muhammad is something you should read, even though it will not really help you with reading the qu'ran.
as for the order.. There is a hadith where someone asks aisha, and she says "it does not matter what order you read it." So yeah. However, I like to read it in the "order of revelation." You will see that a lot of the themes are repeated when you do such.
So yeah, that is just my little advice!