It is usual practice, on a single sided board, to put the traces on the bottom
of the board and the components on top. Makes it easier to solder that way.
On a double sided board, the general rule is to put the traces running one
way on the top and the other way on the bottom (say left to right on bottom
and front to back on top). For your application, if you are going to use a
double sided board, put as many of the traces as possible on the bottom
and use the top as a ground plain. It is OK to put a few traces on the ground plain
side to jump over something if you need to. The goal is to keep traces as
short as possible.
Try to avoid sharp corners, use rounded corners. Keep traces the same width
all the way through the radius.
Hope this helps!
We'd love to see how you improve the design.