There are 2 types of backgrounds: image and starting from scratch. You can use an image as your background, or create your own background with brushes and other materials. Specific types branch off of these two main types. Here are a few for you to use if you can't think of anything:
Stock Image
This type of the background is the most common and quick type people use. This saves a lot of time, but there isn't enough space for a diverse brush usage because of how detailed it usually already is. Therefore, most would use other resources such as patterns, textures, fractals, and C4Ds. You basically just download an image you can use and treat it as a background.
Examples of how they can be used:
Examples of how they can be used:
Smudge or Blur
The title says it all. The contents of the background are smudged. You can brush different colors on one layer and smudge them all, or duplicate (Command + J) an image multiple times (they should completely cover the file), merge all the layers, and then duplicate them. You can also use blur filters instead of the smudge tool. If you're going to use the blur filters, I suggest first trying either Gaussian Blur, Motion Blur, or Radial Blur, which can be found under Filter > Blur at the top of your screen.
Cloud
Another common type of background. This is basically when you use the Cloud effect, which you can find in the Filters tab at the top of your screen (Filter > Render > Cloud). However, you must choose your desired foreground and background colors first before using the effect, which are the large overlapping squares at the bottom of the toolbar to your left. The front square is the foreground, and the back square is the background..