Don't need a sharp film. For b&w, just about any rc paper will do. I also like Ilford ortho +. For optimum sharpness you want a narrow range of sensitivity anyway, so these blue-sensitive materials work nicely for b&w in many cases. For a speed boost, you can preflash the paper or film.
I've also done some pinhole with the 4x5" Fuji 3000b instant film and it is pretty neat to get a print on the spot.
I think the fanciest processing I've used for pinhole was 5x7 Ilford hp5+ pushed two stops. But I like the ortho stuff and paper because it's so nice to be able to develop by inspection. Reciprocity schmeciprocity! Ortho has an additional advantage that it is quite contrasty and this can give the impression of better edge definition / sharpness.