First let me distinguish between the term "action" and "relief". While they are related and relief will affect action, there is a distinction.
Action generally refers to how high the strings are above the frets. Relief also refers to how high the strings are above the frets, but relief more commonly refers to adjustment of the neck to prevent fret buzz. Both will be discussed below.
There is a tradeoff between setting the "action" for optimal sound and tone and for ease of fretting. Each individual guitarist must find that balance that works best for them personally.
If you lower your saddle, you will lower the relief between strings and frets at the same time.
It is worth considering that, while generally they go hand in hand, the string height above the soundboard and the string height above the frets potentially affect the sound in different ways. Raising the action above the soundboard is usually accomplished by increasing the height of the saddle above the soundboard which will increase the torque of the strings on the saddle, resulting in greater movement of the soundboard. Greater distance between the strings and frets will allow the strings to vibrate freely with a more aggressive attack allowing the guitar to be played louder. Also, if the action is set as low as possible for faster and easier fretting, a minor amount of unnoticeable contact can occur which (while falling short of audible fret buzz) will dampen the string vibration just enough to affect sustain.
On most acoustic guitars, raising the action by adjusting the saddle will increase both the string height above the soundboard as well as the frets. However, some acoustic guitars with removable necks could allow for an increase in the string height above the soundboard while keeping the strings closer to the fretboard (lower action) by altering the angle of the neck. Thus you could enhance the volume output from the soundboard by raising the saddle - while maintaining better playability by adjusting the neck angle to keep the action lower.
Some folks adjust the truss rod as a means of increasing the action. This is not the purpose of the truss rod and not the ideal way to set your “action" (string height above frets). In short, the truss rod counteracts the string tension on a steel string guitar to control how much the neck bends. It allows you to apply counter tension to keep the neck from curving too much. Loosening the truss rod will increase the relief in the center of the neck but won't raise the action as much on either end of the fretboard.
Ideally you want to keep your neck as close to straight as possible without fret buzz. You will want a very slight concave bend in the neck giving it more relief in the center. Otherwise the elliptical vibration pattern of the string will contact the frets causing "fret buzz". For more on truss rods and what they do click here
Once you have the truss rod adjusted to properly counterbalance the string tension with no fret buzz, you can raise or lower the action by adjusting the saddle. The height of the nut will impact the action as well, but the saddle is where adjustments to the action on an acoustic guitar is most commonly made.
After removing the saddle (which is held in place on the bridge with string tension) you can sand it down to lower your action or you can add shims to raise it. However, if you are raising your action to achieve better sound, I would start with a new saddle and sand it just enough to reach the desired increased height - because a shim could dampen the transfer of energy from the saddle to the soundboard.
With regards to the second part of your question – many guitarist (myself included) own multiple acoustic guitars set up for different applications. So if you wanted one guitar that was optimized for maximum sound and tone that you would play using mostly open and first position chords, and a different guitar that was more comfortable and easier to play using barre chords in the higher fret positions, you could alter the set up on each guitar for those two purposes.
For your open chord guitar, you can set the action higher with a taller saddle and perhaps use a heavier gauge string set. If you go with heavier strings, you will need to adjust the truss rod for the greater tension of the heavier strings. You will also want to be sure the larger gauge strings will fit properly in your nut slots.
For the easier to play guitar, you would do the opposite. You would want the action set as low as you can get it without fret buzz and you might want to go with lighter strings which will tune up with less tension. Again, a string gauge change requires a look at the truss rod adjustment and string slots in the nut.
Any guitar set up will be specific to the string gauge so you will want to have the desired strings installed prior to making adjustments to the truss rod or saddle height.
Since you have more than one acoustic guitar, it might make sense to set one up with a higher action to achieve nicer tone while playing open chords. If you are going to go that route, you might try to determine which of your guitars already has the nicest tone to your ears and which is already easier to play up the neck and let that determine which guitar to set up for which purpose.
Good luck and enjoy your guitars.