I started systems of equations with graphing because it's the hardest, most useless, and the one I wanted to teach least. I did a bad job on it and they didn't really even understand the concept of 0 or infinite solutions. And when they tried graphing on their own, it went horribly. They suck at graphing. Everyone always got different answers. Here are two of the worksheets I used.
From there we went on to solving systems by substitution. I think this is the easiest method but the students struggled with it more than I expected. They were fine is y = 5 or x = -3 but when it got to y = x + 2 they panicked and made it harder than necessary. And oh lord when we got to x - y = 6 they were clueless. I always had to remind them to get x or y alone. They could do it when they heard that, but they always stared cluelessly when they first saw the problem.
From there, we went to elimination (I stole this ppt). They liked this much better and tried to use it on every problem by default. I don't think we ever got to the point where they could look at a problem and pick which method would work best. Here is a trashketball review game that I stole and modified and here is a quiz.