First rule of goalkeeping: get two hands on the ball. Only if you can't do that do you go with one hand - and if you are going with one hand, then you're already to some extent into "desperation" stage where you'll be happy with any result which doesn't result in the ball immediately ending up in the back of the net.
When it comes to one-handed saves, a goalkeeper generally won't be looking to gather the ball as a result of the save, but instead to put the ball in the safest location possible, which will often be out for a corner rather than allowing a rebound. If you're jumping/diving sideways for a ball close to the top of the goal, it's much easier to push it up and over the bar for a corner if you do that with the trailing arm, as that naturally comes up as you reach your highest point; if you're trying to push the ball round the post, that's something you'll do with your leading arm.
Picking up on some of your comments:
- I disagree going with the trailing arm reduces your reaction time, or at least that this is significant. It's a question of which arm you can get to the ball at all.
- Yes, if the ball is swerving and/or dipping it's hard. On long range shots, it's up to you as a goalkeeper to read the spin on the ball and react accordingly.
- Close-range shots are completely different - in those cases, you don't really have a chance to react at all and are just trying to make your body as big as possible and get something on the ball.