I've raised the action a bit ... but I wonder if it was too much. How much space should be between the string and the 12th or 24th fred if I press the first fret?
There is no "set in stone" value for action... if it´s too low for your style you´ll get buzzing and it will be unplayable, if it´s too high you´ll be working too hard and wont want to play...
Action needs to be set where it "feels" right.... 1.6mm @the 24th fret (measured w/ the string fretted at the first to remove the possibility of a high nut) is definitely on the lower side.
I set my guitar up a little differently. Some guitars I use for slide so I like the action a little high ( slightly lower than 3 16ths). For my "standard guitars I usually set the action at 1/8th. For acoustics they are all slightly higher than 1/8th. I feel you get better sustain with higher action and eliminate any potential issues that will cause the guitar to buzz. However if you play very fast stuff, lowering the action will make it a lot easier. The down side to this is bending will be somewhat restricted if the action is to low. As Zerb said there is no right or wrong..... the guitar has to feel and play comfortable for you.
The problem with using a measurement based on an open string clearance is that if the nut is too high it will throw the measurement out. to avoid this, I tend to stop the string at the first fret and measure the gap at the 13th fret, 1.6mm is probably about right, but if the nut is high then it might be too low.
I tend to work to a default value of approximately 1.5mm for the bottom E and 1.25mm for the top E. I then use these values as a springboard for adjusting the player's personal settings.