Here's an example of quilting diagonal lines both ways through a rail fence:
https://www.pinterest.com/pin/94646029639965354/
Here's an example of quilting diagonal lines one way through a rail fence:
https://www.pinterest.com/pin/436356651368247677/
Here's an interesting examples of using diagonal lines both ways in varying distances from each other:
https://www.pinterest.com/pin/143341200617036770/
For straight lines like the above, I would use a walking foot (assuming you are quilting on a domestic machine).
An allover meander or an allover pantograph design would work well too. I find that loops are the easiest for me to do on a frame setup; probably very easy on a sitdown too. Here is an example of allover loops:
http://quiltingdigest.com/this-rail-...-of-fresh-air/