I prefer to do the french double fold continuous bias, but that's mostly just preference and because I love using striped fabrics for the effect when I'm binding. The biggest need for bias is around curves, and so 5% or so of the time, I do use straight grain for whatever reason.
Straight grain is going to miter just fine around a square corner. I just do the diagonal seams like normal, but you can just butt joint those too. When I can, I like to use the length of fabric instead of the width, just seems to work better for me and I will often make my binding lengthwise if I have that left from a quilt back.