I've had silk in the past and while it is comfortable, I really don't think it adds as much warmth as either poly or wool, mainly because it's so thin. In general, I prefer a light to medium polyester top and bottom for day hikes or overnighters. However, if I'm going to be out for multiple nights, I opt for merino wool. Merino wool is not itchy, sweat tends to migrate into the fiber itself, rather than the space between the fibers, so it feels less clammy against the skin, and it doesn't hold odor as badly as poly. Poly stinks to high heaven with even the slightest sweat and after three or four days it's just nasty. While I'm not going to say that my wool smells like roses, it takes a lot longer to start to stink, it doesn't get as bad, and it washes out easier.
I think most people avoid wool because they've never owned merino wool. Once you use it, you'll wish every set of long underwear you had was merino wool. But that's the downside, it's not cheap. I wouldn't pay more than about $20 for a poly top or bottom, but it's not uncommon for me to spend $45-50 on a wool top or bottoms. As a result, I'd only invest in it for the adults, not growing kids.
For brands, in wool I like Ibex, Icebreaker, Smartwool, and Patagonia. In wool I prefer stuff that's 140-195 grams/meter and find anything over 260 to be too warm for a base layer (you'll sweat no matter how little you have over it in a hard effort). For poly, most of my stuff is from Costco, who carry Paradox. I'm more ambivalent on poly brands and my only bad luck has been with Patagonia in poly because it tends to 'pill' which is purely aesthetic, but nevertheless, I don't like it.
Another thing to think about is flammability. Poly is highly flammable and melts onto skin when it burns, wool and cotton are far less flammable. Personally, I wouldn't buy cotton for warmth as it holds sweat, feels clammy against the skin, and if it gets soaked it will cool you off faster than you can possibly produce body heat that it carries away.
Think about a layering system, not just thermal underwear. Thermals are your base, they're your foundation, but to stay warm you will probably need a layer of fleece or wool over it, possibly two layers on top, followed by a windproof layer over that. As others have mentioned, you need to avoid sweating at all costs, which sometimes means when hiking up hill, you might be wearing nothing but your base layer and a wind jacket on the way up, but at the summit, putting all your layers on for the descent. When I go hunting I'll start the day in nothing but a thermal top and bottoms with my goretex layer over them for the uphill hike in. When I get to my stand I'll add a layer of fleece, top and bottom, a down jacket on top, then put the goretex back on over it all. I also carry a small foam pad because anywhere your insulation is crushed by your weight, you will lose heat at an alarming rate.
Stripping off layers and putting them back on is not something that comes naturally for most folks, but it needs to become ingrained over time in safe environments, where you can get inside and warm, not in a life or death, nowhere to warm up situation and where the consequences of getting sweaty might be life or death. I've been fortunate enough to survive some very near misses with hypothermia a couple of times in my life and they're valuable learning experiences, but if I didn't have the first event to teach me the warning signs, I probably wouldn't have survived the second event when I was all alone and had no one to look after me and get me moving.
