There's no right or wrong way. But every car is different. Most mid to full size cars, minivans and little suv's I've worked on have a full k-frame that goes from radsupport to behind the front wheels. The entire motor and transmission are usually bolted right to the k-frame/subframe. To pull the drive train out it's easiest to drop the works out the bottom. Undo the steering shaft, undo the ball joints, tie rods ends, pop the axles out, leave the spindles bolted to the struts, undo rad hoses and usually the entire wiring harness unbolts under the hood somewhere, remove the exhaust, fuel lines, trans cooler lines, cut the wire someone hacked into the harness for a remote start.
In the Mirage the engine and trans is mounted to the right and left frame rails of the car(probably giving it a higher center of gravity now that I think of it) The subframe doesn't support the weight of the engine and trans. There is a little dog bone mount that goes from the frame to the engine/trans to stop it from rocking forward and back. The control arms, rack and pinion and sway bar bolt to it.
If you want to drop it out the bottom. Lift it high, like at least 3' and lift the entire car cause engines don't like coming out crooked.
Drop the subframe. Make sure you lock the steering wheel and don't move the steering rack once it's disconnected. Mark the shafts before you pull it apart. It's a pain and will go back together wrong. No need to touch the brakes regardless of which way it comes out. Just unhook the tie rods, push down on the control arm, it'll come. Don't use pickle forks to separate joints either! Just google how to do it right using a bfh not a claw hammer. Then pull the spindle away from the car once the axle nut is off. Just let the spindle hang with the strut.
I don't know if the compressor will swing out of the way,(with the rad support in the way) you might have to let the green juice out.
If you go out the front pull the bumper, rad support. It's easy and doesn't take long. Probably looks worse than it is. Bumper is maybe 10 mins tops to remove, rad suppport is only held on by 4 or 8 bolts at the front of the frame rails. No hidden hard to get to anything. I'm pretty sure the condenser will swing out of the way without needing to drain it. should be able to remove the compressor too as it's right there.
I wouldn't worry much about the ac, what's a refill cost under $75?
__________________________________________
View my fuel log 2014 Mirage SE wussie cvt edition. 1.2 automatic: 37.7 mpg (US) ... 16.0 km/L ... 6.2 L/100 km ... 45.3 mpg (Imp)