You control the contrast range on the ortho negative by development and the use of filters when taking (green, yellow). It is the film that is "ortho" and not sensitive to red light. Once you've developed the negative, it should be treated just like any other negative when printing.
The contrast of the printing paper is independent. You control the contrast of VC papers with contrast filters or other filtration (e.g., a color head). Graded papers come in different contrasts, but are getting pretty rare these days. An ortho neg can be printed on any kind of printing paper.
If you are trying to make an internegative, you control the contrast of the interneg itself by development. If you are reproducing a color original onto the interneg, you could use regular B&W contrast filters (like you'd use when exposing a negative in-camera), but with ortho film, only blue, green and, sometimes, yellow filters are effective. Red and orange filters just remove the light that the film is sensitive to and you'll end up with long exposures and skewed tonalities. For black-and-white originals, just control contrast by development.
Film and paper are separate things.
Doremus