Speed - just dig straight. It's the only real option for speed.
Survivability - nothing beats the Lucky Horseshoe. New accessories would allow you to brake your fall late, but it would require some to moderate effort on your part and that's not as good. Sans Horseshoe or new tools, you have to resort to something like a pool at the bottom (make it deep, a couple of body lengths). I don't like that method myself. If you want to prevent monster damage, just build side walls whenever you hit natural caves. Make it a tube all the way down.
I wasn't sure if you wanted to avoid spoilers but climbing claws/shoe spikes allow you to slide down walls and you can wall jump a little. They can be combined into an item that allow you to cling to walls. Again, using this requires you to time the end of your drop which IMO is not ideal. The Umbrella, when actively used, slows your fall. Its available in wooden chests now, as are the claws/spikes.
Lastly, Rope can be used to fix the falling issue. 10 pieces of role can make a coil, which is useful in part because it can be placed and it takes up 10 sections, saving a little bit of effort. You can line one side of a hellevator with rope and create an easy solution to get down. IMO, it's not hard to get a horseshoe and that's still the preferable option.
Ease to Build & Tools & Immediacy - Unfortunately, the ease to build is something of a relative notion. It's going to take you time no matter what, and there is no way to mitigate that (but see below) You are digging straight down in a shaft two tiles wide. Pre 1.2, you would have been crazy to try digging with anything less than a Gold Pickaxe. It's the first one that reduces the # of hits to break stone to 2 (from 3), and dirt to 1 (from 2). Even in a small world, you will be digging through a lot of stone on the way down and anything worse will drive you crazy. Allegedly, some of the new pre-hard mode ores make better picks, but I can't comment to the particulars at time.
If I get lucky on early spelunking then I make a gold pickaxe (lucky = easily reachable gold deposits, gold bars found in gold chests). Otherwise, I usually farm the Eater of worlds a little and get the nightmare tools + good armor. The nightmare pickaxe is ultimately the same as the gold (same speed; slightly increased digging power but not enough to matter). This takes more resources up front (building an arena, money for bombs to mine down to and destroy shadow orbs unless you luck out and get enough mats for worm food) but there is no guarantee you'll come away with enough gold for the Gold Pickaxe after significant spelunking. It takes 12 gold bars (48 ore) to make it. The Platinum Pickaxe is slightly more powerful but not enough to make a difference in whacks needed to remove a block.
You don't need any other resources for digging the actual hellevator. you may need resources to build a hell bridge but you just picked up a crapload of mats on the way down so you are set there. Getting to a sky island does require some extra time spent chopping trees, but we're not talking about a lot of that.
There were also pre-release rumors of new types of tools that could help but I have not found any evidence of them yet. I will update this answer if I find anything.