When transposing a song to a new key, do I use a 'sharp' or a 'flat'?

Best explanation I have seen HERE

There are conventions that essentially govern which keys are called what. I honestly can’t tell you why (although my gut tells me it’s whichever key has less accidentals), but I’ll give you a list:

Bb, not A#
C#, not Db
Eb, not D#
F#, not Gb
Ab, not G#

It all depends…...Db is easier to read.
Guitars are used to sharps.

A sharp has so many sharps to read it’s hard to think of it.
BEADG are the first five keys with flats. and F which only has B flat.
GDA read sharps.

Have you seen http://chordie.com/

Doesn’t matter… means the same.

They are exactly the same musically, but look:

Transposing a song from C to A# would mean that you have the following notes:

A# B# (=C) C## (=D) D# E# (=F) F##(=G) G## (=A)

Even if you simplify this, it would still be:

A# C D D# F G A (which is in fact a wrong way of writing these notes)

Wheras in Bb the notes would be:

Bb C D Eb F G A

even without the need for simplification. This is why, as cfrydj said above, we prefer certain options, since they mean a clearer and easier to read sheet. Both are correct, but use common sense and pick the best one.