There are so many chords that you can use in Jazz Music. Like Major7 (maj7/M7), Major9, Major11, even Diminished which have a form like 1-3-5-7 in maj7, 1-3-5-7-9 in maj9, or 1-b3-5-7 in min7.
There are so many genres of jazz that have different chord to use. Like bossa-nova, they play basses just the 1st and 5th note. Swing, they do walking bass which a pretty difficult. Because you know nothing about jazz genres, you should check it out in youtube players like: B B King, Ella Fitzgerald, Basia, Erroll Garner, or search it in iTunes. After that, you can pick which jazz genre are you. Perhaps you can try fusion jazz or because you're new to this, try Folk Jazz, Cool Jazz or Free Jazz.
For composing a song, people often have a walk in afternoon, night, or morning to get some inspiration, that maybe can become a new composition.
You can use chromatic scale in your composition. So your song won't become mainstream to your ears. The point is: jazz is free genre, you can express your feeling via your instrument. I think the best way to answer is: pick your genre first, and then ask again if you don't understand something.