I absolutely start with secondary knowledge--whether it's reading, a lecture, a conversation, a HIGH QUALITY introduction to a published source in translation (not all of them are good enough). First of all, seriously, why reinvent the wheel? Previous scholars have done enormous work to put together this particular snippet of information with all sorts of other evidence to understand the time period. If my goal is to understand it as well, I'm going to gain far more from knowing where/how the source I'm reading fits in, than trying to redo all the detective work with only one sliver of evidence.

Also, there is the problem--at least for the medieval and early modern eras I'm familiar with--of understanding the sources themselves. For example, a medieval "history" book (historical chronicle) isn't a modern history text, and if you try to read it like one you will get a very wrong impression of what that evidence actually tells us about the Middle Ages. What is the purpose of the text? How would its readers have understood it at the time? Those questions generally require at least some secondary knowledge.

I read primary first, then secondary. The primary reason being that I don't want the secondary source to color my view of the primary source. Once I have read the primary and have evaluated it, I can move onto to secondary to see how my thoughts do or don't line up with others, and how I can squeeze an article out of the difference. Granted, this applies to my field only, and it becomes hard when you're deep in the field as it becomes impossible to view a primary source as an independent entity because you're always reading within the context of something else.