"Take a photo" is the way we say it 99% of the time. "Shoot a photo" sounds more professional. Models have "photo shoots" with professional photographers. It is only common within a context like that. "Capture a photo" to me sounds very technical. Like something that the manufacturers of cameras would say. Not at all common. That is how the three sound to me.

Taking and capturing a photo have the same meaning, although people in the U.S. generally use "take." "Shooting" is used more often when speaking about professional photographers; we might say a fashion model has "a photo shoot" (noun), or that a photographer was paid to "shoot their wedding." Hope this helps!