You can do any of those things. First, you need to decide what you want the finished quilt to look like. Random lines will not give the eye something to focus on. Stitching lines in an order will give an overall look to it. Doing triangles or other geometric shapes in different sizes and overlapping would be sort of mix of the two things. A lot of quilting is simply straight lines in some order. I think that if you are going to stitch straight lines over a long distance, you'll need a way to keep them straight. Mine would end up wiggly!
I don't know about starting in the middle and radiating out to the quilt's edge. Seems like the lines in the middle will end up being quite dense. I've never done that.