With the way we'll end up digging in the future I'm expecting railway/minecarts to be added within 2016. Red51 said it's of higher priority so we'll see something to do with railway possibly late 2016 at this rate. Making me curious if mine-related, or if it'll be topside, or both.
As for the minecart mining side of things I would expect both 1) A pully system - 2) motorized engine making use of coal, steam, & eventually fuel.
Not sure how Red51 wants to work the wired minecarts, yet could expect something along the lines of turning wheels + wires going from it, attached to tracks themselves, heading down & then looping back up (if you have another pully wheel below). I doubt we'd have powered rail boosters because this isn't Minecraft, yet we could instead have 'highspeed rails' that could work similar. Something meant for higher grade speeds that once you tech-up to a higher tier train type you would be able to go quicker.
Also stumbled across an image that if we're allowed to have 'bulky' mining cars that we should have these that behave like land-rail barges - https://commons.wikimedia.org/…st..._-_NARA_-_540955.jpg . Imagine how much stone, ores, & crap we could haul with this from below to top side, and from one settlement to the next. Nearby, of course.
As for elevators, I'd expect them to work as you would expect them to by gradually lowering & raising you and contents on it. I even love the mention of elevators aimed directly at minecarts so you can lower & raise them in both an empty & full state. Would make for interesting mining operations.
[I can't search for 'Minecart pulley' because Minecraft ruined the search results. Can't seek out what I once saw earlier.]