In a plain weave rug, it’s the colours and textures of the weft that really make the look.
If you want vertical stripes on your rug, use the rep weave pattern. In rep weave, the warp threads can hardly be seen from under the weft material. The rug will be very densely woven and thick, so make sure you have plenty of weft material. You can also combine the plain weave and rep weave patterns in the same rug.
If needed, the warp can be made narrower.