Here a simple way to create a background texture with halftones:
- Create a new file in Photoshop. I created a 600px x 600px at 72 dpi file for this example.
- Fill the background with 50% gray.
- Choose Filter > Pixelate > Color Halftone. I left the default angles alone and chose 8 px for one sample and 30 px for the other.
- Choose Image > Adjustments > Gradient Map and pick whatever colors you like.
- If the background you've created has too much contrast, you can apply levels or change the layer opacity to get the desired result.