So, I’m getting into developing 2D Platformers and I use Photoshop to make characters and character sprites. I was wondering when I making a Background Image for my game
, is there anything I need to keep in mind like the size the background image should be and if so do you have any recommended sizes? Or does it even matter what size my background image is because I know you can change the size in unity, and will it mess up the background image resolution?

It would depend on your target resolution. You can scale it up or down, but you may lose quality.

Another thing I would look into is how your background is going to work with the game. Is it static, does it move or scroll, is it a parallax? Because that might require some design differences to make a repeating background.

Like this for example: Recorded Video Sessions on 2D in Unity 4.3 - Unity Learn