The bad thing about fabric is that it stretches. The good thing about fabric is that it stretches. I never worry about whether I have the warp or the weft facing a particular direction. After all the good thing about fabric is that you can nudge (stretch) it a bit to fit. Starch helps keep things stable as well. The only time I really fuss about stretch is when I'm cutting and sewing off grain like bias or fussy cutting.
A technique that I use for fussy cutting if it is terribly off grain is that I draw the shape that will eventually be my raw edge (1/4" past the seam line) in the position that I want it on the fabric and cut a larger piece quite a bit beyond those lines. My cut for the larger piece is with the grain of the fabric. With my raw edge lines drawn on the fabric I match up that line to the adjoining piece raw edge and stitch a 1/4" seam. After I have secured all the edges of my fussy cut piece I trim the edges to match the adjoining pieces. I find the larger piece doesn't stretch as much as if I was working with a cut raw edge off grain. Hope this make sense.