In jazz, let's say, how would one choose a key signature for writing a lead sheet for a song where keys change every few measures or faster? Is writing the key changes explicitly going to be helpful or distracting? And if it isn't helpful, should you just choose C, and just label accidentals as they come up? What's best for a player to read?
This depends on the circumstances, but I would suggest it is more common to write no key signature (or the best closest match like "F" if all B tends to be Bb.) especially in the case of changes that last only a few measures. Here are my reasons:
1) It's not normal for jazz music to include alot of key changes written as new key signatures. This will happen if a whole section (consisting of 8 measures or more, for instance) is in a different key, but I think it's the exception rather than the rule.
2) Writing a key signature is more than just a matter of ease and convenience for displaying notes in the simplest fashion. At its core, writing a key signature communicates that the tonality of the piece has changed and in jazz music there is a high tolerance for temporary adjustments of tonality that are not interpreted as key changes.
3) Many sight-readers will be more confused by lots of key changes than by lots of accidentals.
If you look through the Real Book, or transcriptions of jazz solos that may also help you get a sense of what the conventions are. In general, though, there are no hard rules and there may be multiple solutions that are technically correct. I think it's best to defer to the norm and also to what your players expect. If you write the music in a way that they find unnecessarily difficult, be prepared to hear a few complaints from them. :)
I'd say to write all the key changes. Average sight-readers should be able to glance at it and instantly recognize it and reposition. If you're writing accidentals then they have to check every single one. That isn't a problem for experienced sight readers, but it's still more work.
In this case, as someone who sight reads jazz, I would definitely agree to start with the first key and write key changes within the song, unless it's very often. there are certainly some songs that are written all in accidentals a because there simply is no key for the song.
if the key changes are helping the ready by providing a clear view of what's happening, write the key signitures. if the changes are hurting the reader because the chart is cluttered with a key change every few bars, leave it out. Use your best judgement to have the cleanest, most obvious, and most clear chart as possible.
It depends how much and how often the 'key centre' is going to move. Any piece will have what most would call a 'key centre' as in the start or finish sounds like home. This then would establish the key for the piece. A key signature would then be helpful. For changes of a bar or two, usually accidentals are used - they tell the reader that something has moved, but will come back to key at some point. If the modulation is for,say, 4 or more bars, then a key change is probably in order, so the reader can 'change hats' for a comfortable time.I'd also say that note changes for a bar or two would be better accepted if they followed the original key, as in start with flats, try to use flats. But there are some readers who prefer the 'correct' notation with sharps in this case, because they see better where the music is going.