I've made the mistake of digging straight down a few times, but I've learnt my lesson now.
I usually keep a few wiki pages open to tell me what I need to know crafting and advice wise.
Haven't checked out the nether, my picks never seem to be able to do anything to the material you need to make a portal.
As for building projects, so far I've had two major projects; my initial base. I decided to dig into the ground for my first base, but eventually I added a tower some fortifications and a few rooms etc. Then I added a few mineshafts.
My second building was an island fort. I reshaped a small island and build a pretty naff castle on it, three floors above waterline, dock to the side to make getting into a boat easier and a sand trap above the only way in. I've also got overhangs all around the edge to prevent spiders getting in.
I also tend to keep my main mine shaft within the base.
Was just wondering, what's your process when you work a mine shaft, I tend to head straight down till I hit something interesting, then I leave a shelf and mine down some more, eventually I hit a cave opening which is where my shaft finishes. I can then work back up, digging out a tunnel at each shelf till I find more caves. Once my tunnels are done I start on the caves. I also make the roof of my shaft glass so that when I'm at the bottom I can see whether it's day or night.
Do you have a "kit" you carry when playing?