I try and use the straight of grain, selvage side. It really does make a differnce. I worked for a shop that did custom dressmaking and alterations for a while. I learned a whole lot about what makes a project work and what doesn't. Using the crosswise grain is how you end up with wavy borders. By the same toke the crosswise grain or even bias makes it much easier to work with curves. It allows you to fudge your piecing more succesfully.
Always remember that fabric is not a stable medium.