Should I write F# or Gb? It depends on the context. Here are some guidelines.
In a melody
stick to the key signature where you can. Accidentals should deviate no more than a semitone from the key signature. If F# is in the key signature you can write Fx (double sharp) or F (natural) but not Fb.
Have a good excuse ready before you write a double flat or double sharp. G is almost always preferable to Fx. Use Fx in preference to G only when G# is prevalent in the melody, or you have some other good excuse.
Lean towards principal note names. Rare names like B# and Fb should be used only when there are four or more sharps (for B#) or four or more flats (for Fb) in the key signature.
In a chromatic run
run up in sharps and down in flats.
In a scale
write your accidentals so the musician recognises the scale.
In a chord
write the chord so the player will recognise it.
Give chords to players that use chords (guitarists, pianists and soloists). Don’t worry instrumentalists with chords if they won’t be needing them.
Guitarists and pianists map their physical position to the chord. When they recognise the chord they relax to it. Give them the chord and you give them the freedom to improvise (unless “Strict” is written or implied).