When using a billboard(Image on a plane) as the background this is commonly called a flat. As for lighting, usually you don’t use an HDRI with a flat. You just setup light objects and turn off receive shadows on the plane. Depending on the image and look you’re going for, you can use the image as an emission texture on the plane. Some artist will use an HDRI that matches closely to the feel you want from the lighting. If you’re working with an environment team they will sometimes go all out and create an HDRI/Skybox/Sky-dome. Basically you place the camera at the world origin and rotate it 90 on the X axis. Then build your background around the camera. Then you set the camera to Panoramic(This only works in Cycles) then set it to Equirectangular(Equirectangular Cube face if you’re going skybox route). The default setting work for 360 degree background. Change Longitude to -90 to 90 for a 180 degree background. Then change output to Radiance HDR file type. Note: the dimensions need to be a a 2 to 1 or width needs to be twice the size of height. also it works best if it’s a power of 2 like 1024 instead of 1000 for example. I personally don’t create full HDR render, and prefer just the plane or a grid with simple flat shapes.
