A misting system is fantastic, but do NOT get a cheap one like a monsoon or a reptifogger. They have bad reputations for breaking and flooding. Save up for the mistking, but they cost about $110. Misting systems are wonderful since you can set them to run automatically, but they are not required if you mist by hand and use a dripper.
For now, get a Little Dripper. They cost less than 10$ and you can get it at any pet store. Adjust the nozzle to get about 1 drips a second, no more. It will seem slow, but remember, your Jax is a tiny little guy. Sit the dripper on top of the cage and position it so the drips land on a vine or leaf where he can sit under it. You'll need something to catch the water. You can use a shallow bowl or fresh paper towels every day.
Some chameleons prefer drips over misting anyway. My Jax always preferred dripping. Then you can mist once in the morning and afternoon for a humidity boost. Adding a dripper will let your chameleon have access to moving water all day without worrying he will drown.