Normally I dig out a base to stash my initial supplies and grow crops, then as I start to dig out stone, I build up a massive stone tower, which is where my rooms actually go (In fact, I find this solution more convenient than digging out rooms in the rock, albeit the reason behind this might be that I tend to favor maps with an aquifer and a magma pipe to dig through it, and thus I would have to dig the rooms quite deep.
It depends, though. My last fortress was in a frozen tundra, and while I intended to build up a tower as usual, the undead hordes prevented me from doing so, so I instead dug out a small underground "bunker", with blast doors (risen bridges) and automated defenses (this made the inside of the fortress pretty safe, barring mistakes, but you still have to go outside to fetch stuff, and the sheer ammount of casualties that I suffered ended up in generating a terminal tantrum situation). I intend to reclaim it, eventually.
My current one is built over a volcano, and I intend to build a palace-temple at the top, and then more buildings every level down, all out of green glass (well, barring some purely structural pillars of obsidian I've built just underneath the main glass structure. I know that it would hold no matter what, but for RP and aesthethic purposes I try to avoid blatantly absurd structures (castles hanging onto a single floor tile, that kind of thing). Goes without saying that there will be one (more likely several) sacrificial chamber(s). Oh, and as a challenge I am keeping the nobles alive, because this is supposed to be a capital of sorts. So I try to fulfill mandates (barring the impossible ones, such as an adamantine mandate I just had, when I have NO adamantine...)