You do NOT want to dig into an aquifer from below. remember that an aquifer is an infinite source of water, and water flows down.
Yes... we SEE only one Aquifer level in the opposite cliff, but that only means that there is one Aquifer level that extends as far as the cliff face. There could be others, on different levels, that stop short of reaching the cliff face. Whenever possible, you want to dig DOWN, not up. There is no warning at all when you approach an Aquifer level from below. You just die. And so does anyone on a level below you.
On the other hand... if we can avoid killing ourselves, an Aquifer is an insanely useful thing to have. It supplies a source of fresh water (absolutely required for wounded dwarves) free of infection (which you can get by treating wounded dwarves with impure water) which is indoors and protected by our fortress. It is a source of almost limitless mechanical power, for running Magma or Water pump-stacks, Corridors of Spiky Death, food processing machinery, etc. It allows us to set up fluid-logic computers (flip-flops, latches, timers, switching circuitry, etc), to control automated defenses (such as Magma Fountains or the aforementioned Corridor of Spiky Death).
Setting false modesty aside, I have become something of an expert at designing and constructing insanely complicated machinery out of basic in-game components such as Gears, Axles, Pipe Sections, Pumps, Floodgates, Drawbridges and so forth. My Orbital Defense System was very well received on the main Dwarf Fortress forum, and in previous games my Pressurized-Magma Fountain (which shot flaming Magma over 100 feet into the air, to rain down on the beardless heads of our enemies) was rivaled only by my infamous Corridor of Spiky Death.
That's why I usually choose a Mechanic character to play.