Your guide is correct. I think a Nikon FM2 (as MAx mentioned) and an appropriate manual focus lens will do. No batteries needed except for the meter. KEH has one for $132. Get that. There are other choices but this should work well. there are equivalent choices from Canon, olympus and Pentax. Use negative film and NOT slides. Film has a significantly wider exposure latitude (more forgiving)
Although you may be able to succeed with a DSLR, there is a HIGH probability that you will get no pictures with one. If you are going on this trip for purely photographic reasons, have great expertise with digital cameras in this environment and are willing to expend energy babying the camera equipment, the DSLR may work. I doubt that is the case.