No, don't worry about CYA (stabilizer) just yet. You have to kill the algae and metabolize the ammonia, and stabilizer just slows it down.
The Borax will also add borates to your water which helps inhibit algae growth, too.

You WILL need stabilizer, but that's to keep the sun's UV from breaking down the chlorine too quickly, and for a few other issues. For now? Not yet. You cannot go wrong following Ben's advice.

Carl