Wool was indeed recommended for undergarments, particularly combinations/union suits. It was "discovered" by Dr. Gustav Jaeger in the 1870s that different people had different "specific gravities" - he determined that people with low specific gravity were more likely to get sick, that internal fat and water led to a low specific gravity, and that wearing his "normal clothing" of only wool (especially knit wool) helped prevent this by warming the body and absorbing its moisture. His ideas are well summed-up in The Scientific American, May 1884. Not everyone was convinced (linked is a skeptical bicyclist writing in to contest the claims in the Cyclists' Touring Club gazette), but many did agree at least that wool did a better job than cotton or linen of wicking away sweat from the skin during athletic exertion. (Fashion in Underwear: From Babylon to Bikini Briefs, by Elizabeth Ewing, is a good secondary source on Jaeger's "Sanitary Woollen System".)

Silk underclothing does not seem to have been very popular. I don't really find it referenced until about 1890 - which is when women's underwear in general shifted from being commonly made out of a heavy cotton longcloth to finer, softer cotton fabrics. The Illustrated American in 1891 repeatedly references silk chemises specifically in the context of bridal underclothes; The Woman's World in 1888 also brings them up only when discussing trousseaux (though a reference to silk crêpe chemises becoming popular is difficult to understand - popular for trousseaux, which are the point of the article? Or popular on the whole?). The same issue of The Illustrated American, however, also brings up sets of China silk nightgown, chemise, and drawers without any bridal references - as these reportedly cost $35-40 (for $45-50, you could get a petticoat as well), they would have been affordable only to the wealthy unless made at home, as the writer describes. More practically, knit union suits (the stereotypical old fashioned long underwear, worn by men and women) could be had in wool, silk, or cotton, although I don't know how much of a price differential there was between the fibers.

However, when looking at the pieces that are still extant, underclothing at the end of the end of the 19th century appears to have been largely made of cotton. Linen was almost universally used for shifts and shirts in the 18th century, but as improvements were made to cotton processing, cotton became cheaper and linen more expensive. Cotton supplanted linen in this area over the course of the second quarter of the 19th century - although it's not as cool or smooth as linen, it was easily washable and cheap; both qualifications were important, since the main purpose of the undergarment was to soak up sweat and body oils to protect the outer clothing, and you would want as many as possible so as not to feel pressured to have the laundry done frequently. Silk is kind of a pain to wash and so was not practical at all for this use, although in the 1890s there are many references to "washing silk" - pongee, senshaw, tussore - which may have come into use at that time and facilitated the apparent rise in silk underwear.

There were a decent amount of silk petticoats at the end of the 19th century, though. Not being worn directly on the skin, it didn't matter so much that they were difficult to get clean, and not being worn on the outside, they didn't have to be very nice silk or very well made. The crisp scroop of a silk petticoat was something to aspire to in the 1890s, when skirts swished against the legs instead of being draped over some kind of support.