What type of camera would be best for this task?

I was working under a director/camera operator, and I noticed that while shooting downtown at night, he can get the footage, to look really bright, and really good, with a low amount of noise, since we were shooting documentary style, under natural lighting mostly.

I noticed how in his camera, everything is in focus at night, which is the complete of the cameras I am use to. I am use to ones with a really shallow DOF, especially under low light conditions. But I like how he can open the aperture all the way up to f1.8, he said, and it's still all in focus.

I would like a camera that can do that at night, when it comes to shooting scenes with a lot of action in, where you would want a lot in focus.

But I also like shallow DOF as well when it comes to the more quiet scenes, and dialogue scenes.

I was wondering, is there a camera, where you can have the best of both worlds, without having to spend the extra money on a 35mm adapter, to get shallow focus? Mainly I want a camera, where I can go from a deep DOF under low light at night in the city, but also go to a shallow DOF as well, without light being the dictator in what the DOF should be.

But is there a camera that is low cost, that can do that?