okay, cool.
How many places on the neck can you play each chord? Are you able to extend the chords or are you sticking straight to the chart? What are some of the tunes?
Each chord is an arpeggio possibility...I really think arpeggios are the most direct route for a jazz beginner...so hear me out on this, and I'll talk about modes/scales too.
So either method is a roadmap...the thing that makes jazz sound, well...jazzy, is changing what you play to fit the chord of the moment. So over a Cmaj7, for example, C, E, G, and B would be target notes, with the third and seventh really defining the quality of the chord...these notes are really just there to give you possibilities--good starting and landing places.
If you're interested in this route, I have several videos on my website about a chord tone approach...again, I find this the most direct route for jazz beginners. If you include chromatic passing tones and colorations in the chords beyond the seventh, you can get really tasty advanced lines that directly connect the chords. So basically, if you know how to see Dm7-G7-Cmaj7 on a chart and can think Dm9-G7b13-Cmaj9 or Dm7-Db7#9-Cmaj#11 on top of that, you can get some great sounds...
Now, using scales and modes well is a more advanced way of looking at things, IMHO. Basically what you are looking at is something called Chord-Scale-Theory. or CST. You basically need to know how each chord is functioning in a group and assign a mode or scale to the chord...a lot of players who use this aren't necessarily thinking about just the major scale and it's modes, but the melodic minor as well. If a mode/scale approach is more your bag, you'll want to brush up on the melodic minor.
So taking that same chord progression of Dm7-G7-Cmaj7, the most basic way to think of it is Dorian, Mixolydian, Ionian...but you'll see pretty quickly that that sounds pretty "vanilla." You might instead think about Dorian, an Ab Melodic minor on the G7 (altered scale sound) and Ionian or Lydian on the Cmaj7...and that's just ONE way of thinking about it. As you can see, that gets complex FAST...
Anyway, I hope this helps...