As a rule of thumb there is the following:
1) Take the key that is nearer in the circle of fifths.
This provides the bigger number of common tones, and therefore avoids some uncommon enharmonic steps.
2.) If the resulting key comes with too many accidentals, change the new key enharmonically.
3.) If the enharmonic result is the same, there can be other aspects.
E.g. if there are some specific chromatic notes (or harmonies that leave the key) that are used very often, this can be an additional factor.
-> Some examples:
In your case, g#-minor is nearer to e-minor than ab-minor would be (in the circle of fifths).
Also, this results (due to the common notes) in a more "natural" interval e-g# (a big third) instead of an unusual "diminished fourth" e-ab.
If you would go on from g#-minor, according to rule 1 you would choose b#-minor.
However, that has too many accidentals, so you would take (according to rule 2) c-minor.
BTW this method doesn't contradict what chillbot wrote:
In his example, d-minor has the same distance in the circle of fifths to g#-minor as to ab-minor (since it's a tritone-relation). However, ab-minor would have more accidentals.
In the case of the transition from C-major to F#/Gb, both variants come with 6 new notes (only B - or in the other case F - remain). Also, both keys have 6 accidentals.
In this case, for strings i would choose F#-major.
Because of the tuning c-g-d-a-e of the strings, the notation in F#-major prevents the players e.g. to play an Ab on the E-string, or a Db on the A-string.
For the piano, i would make it dependent of the overall melodic profile.
E.g. the step b-f# is a bit more intuitive to read than cb-gb, however, a#-e# is less intuitive than Bb-f. Basically, it doesn't matter if you take F# or Gb.
As a last case, if you write for instruments specifically that transpose, keep this also in mind in those critical cases.
E.g. if you write for five clarinets in Bb and three Oboes (which don't transpose), it would be Gb.
Why?
In the clarinets' parts, F#/Gb-major would correspond with Ab-major.
In the case of F#-major, the "correct" transcription would be G#-major, which one would change enharmonically to Ab-major. So that would make no big deal.
However, if you would look at the score, it would be easier to bring the voices in context.
E.g. it's easier to see that C-Bb-Ab in the Clarinets is in unison to Bb-Ab-Gb in the oboes, as if would be notated as A#-G#-F#.
A final example to the rule 3:
Let's take again the F#/Gb-major scenario, and imagine that your melody often makes use of the mixolydian 7th and you also use the minor chord of the tonic.
When written in Gb-major this would be Fb; and in the chord of the tonic the notes Gb-Bbb-Db.
With F#-major this would be E and F#-A-C#.
Now Bbb is a really ugly one, specially when compared to A; and E is "easier" to read than Fb.
However, if you had a piece in F#/Gb-major that relies heavily on the minor subdominant, this chord would read as b-d-f# in F#-major and as Cb-Ebb-Gb in Gb-major.
Now, Ebb usually hurts in the eyes...
But i have to add that these scenarios are highly hypothetical, usually every variant comes with "ugly" note names, if you make use of lots of chromatic notes and stick to the correct enharmonic notation.
The latter you should always do, specially when working with classically trained musicians.
If you have the third of E-major (which is g#) and approach it by a leading tone, this has to be notated as Fx [and not as g]. So the musician intuitively sees the function of the note and usually will provide a more plausibel line.
