At my previous employer, the largest 737 operator in Europe, you could only accept a visual if you had briefed it and double briefed it, and you had to be lined up with the runway at 4nm out. So in theory, if you hadn't briefed it, you could not accept..
Fortunately, at my current employer were happy to accept a visual and the only requirement is to be stable at 500ft. Of course, once we accept we will keep eachother in the loop about the intentions and course of action.
If the minima were already set for ILS we don't change it. If we planned a visual most guys will put 500ft AGL as a reminder to be stable.