For the lower body, I like a thin layer next to the skin. Also full side zips. On the uphills, legs can produce a lot of heat, and you want to be able to ventilate and get the heat and sweat out.
For the hands, I second mediclimber's comment. I have borderline Raynaud's, and anything even slightly tight on the hands makes my fingers go numb in just a few minutes, even in temps like 40F. Loose liners and windstoppers are good. (Overmitts go on the outside.)
In overmitts, look for good waterproofing. Again, I second medi on the soft shell stuff; it's good almost all the time. But on hands and feet, I want hard shell, waterPROOF, no questions. Always have hands in snow, grabbing branches, etc. Very easy to get wet, and then the nonwaterproof gloves are shot. Also, always bring a spare pair, maybe 2. They're weightless and they compress to nothing, and you'll miss them if you don't have them when your primary handwear gets wet.
As far as insulation, it depends on the temps, and on your hands. If your hands get cold easily, or if you're planning a really cold trip, consdier mittens rather than gloves. They're a little fumbly for climbing, but for straight hiking they're OK. Also, chemical hot packs. Weightless, take up no space, and they change the whole picture!
TCD