Jazz can be fairly difficult to write for, especially if you want to go into experimental jazz which I’m not because in there lies madness. Jazz is usually built on instruments playing a simple phrase and then having another instrument. However it is recommended you not play the same idea more than once, depending on the type of Jazz you are aiming to play
For Jazz I would recommend using woodwind instruments and instead of a bass guitar have a double bass because tone is just so much nicer than a bass guitar.
Your best bet with writing a jazz piece is to have accompaniment playing something in the background (be it funky or a depressing parts) and have everyone play that idea, once you have played it then have solo instruments on top. The solo instruments usually are trombone, guitar, saxophone or drums
For chord ideas you can used diminished chords on a regular basis, 7th’s, 9th’s, 6th’s, 6 & 9th’s, 11th’s, 7th’s with flatten 5th’s and finally 9th’s with flattened 5ths. However with Jazz guitar chords there is so much flexibility that the choices are endless
For jazz drumming is a bit more difficult as it depends on the mood you are trying to set. For a funkier piece consider reading up on this but I warn you Jazz drumming is probably the hardest drumming type and I would not recommend a beginner starting there. However if you are going for something maybe moodier or classier then learn to love the high hat pedal and double tapping the high hat and playing quietly. These are very common features of basic jazz drumming but I strongly advise new writers to not write for jazz drumming at all as it’s the hardest type as most Jazz drumming is not written out
Advance features worth reading up about are modes which are very useful for improvising which is a heavy impact on most Jazz especially for advance levels of playing where the drummer becomes the leading instrument
Artists include; Turnabout Jazz Soul, Charlie Parker, Dizzy Gillespie, Frank Sinatra, Wes Montgomery, Herbie Hancock, Chick Corea and John Coltrane.
Jazz has a very wide range of topics and singers however you should take note of skat soloing where the singer usually sings off beat just skating is very common with Jazz singers. It’s very hard to explain without seeing it but just look up skat solo on youtube and you’ll see
Jazz bass is hard to write for usually because it is all improvised but arpeggios and scales are usually the key to a good bass line. Bassist usually get a solo in jazz songs so I suggest using the jazz pentatonic minor scale for this but go with the flow is the main point of jazz and improvising so try looking at other artists for this such as Scott LaFaro