I usually dig straight down to a cavern layer and begin building there. I like the added challenge that walling off a section of the caverns provides, and it's good practice for glacier embarks. I like that I can embark just about anywhere on the map without adjusting my strategy much. (Aside from some military and a doctor for evil embarks, of course). I don't need a river or trees, for example. I have a long three tile ramp leading down into the depths to allow trade caravans to descend, and I often leave some guard dogs and a bridge near the surface to seal everything on the surface off if an invasion comes. The biggest risk is that the cavern layer is dead, meaning I need to import wood or run all the way up to the surface to get some (assuming I embarked somewhere with trees). Even this is rarely an issue, it just means that I'll have comparatively boring scenery and it'll take longer to get beds for everybody.
Occasionally I've actually started a fort all the way down to lava in order to get decent forges running. This is, of course, absolutely impractical. Hauling all of your goods to the bottom alone occupies most of my time when I do this. This isn't as bad if I build in the first cavern layer, so I usually do that. On the plus side, this means charcoal free forges in your "main" fortress without using a volcano.