I've been doing pinhole for a fair bit, and sometimes do paper rather than film.

My favorite paper is Agfa Multicontrast Classic. I also use it to print on sometimes. Both in the darkroom and in the camera, I find it to be a somewhat lower contrast paper than many others. As several have observed, the challenge is to tame the contrast.

The other benefit of this (or any other) variable contrast paper: You can use a green filter to reduce the contrast further if you need to.

My ASAs tend to be about 6 outdoors with no filter; 3 with the filter. Indoors, no filter, I'm about 3, and 1 1/2 with a filter.