The easiest designs to print have white backgrounds, a good margin between the printing and the edge of the sign blank and don't require tight registration between the colors. At this stage in your screen printing education, I suggest that you don't make your own screens. Most screen-printing suppliers offer finished screens with the design already imaged on the mesh, ready to print. When you order the screen, specify the inside dimensions of the frame, the mesh type and mesh count, and explain how you will provide the design to be printed to the screen maker. Novice screen printers often make big mistakes by ordering their screens too small.
Smaller screens are less expensive, but they are devilishly hard to use.
This is the minimum size. The mesh type should be monofilament polyester, and the mesh count is determined by the type of ink you will be printing. After selecting the sign blanks, ask your screen printing supplier to suggest a type of ink. Then ask for recommendations as to proper mesh count. If the supplier recommends a range of mesh counts, select one at the lower end.