I need help finding all the parts needed to do this repair.

Thanks for posting. I agree the 39-315 looks correct. Just make sure the dimensions listed below match what you have. As for the accessories, one reason why we don't sell these parts as bundles is because there's a lot of exceptions with this hardware. The stud bracket used in one window may be entirely different in another case; not to mention, if your old bracket is undamaged you usually can just reuse it. The 39-316 often uses the 39-545 or 39-546 brackets, but I highly advise looking at your old brackets to confirm one of these matches what you have. For the handle, the 39-114L should do the trick. Let me know if you have any other questions. 

Alternate image for 39-315

Yes, we also sell the 39-105 detach clip, which can connect the 39-315 operator arm to the stud brackets we talked about. I apologize for not mentioning that in my previous post. 

That said, I want to stress that I can't say with 100% certainty that these are what you need based on a photo of the operator alone. The 39-315 operator is compatible with a ton of different brackets, clips, and everything in between, and they are far from universal. You've only shown me one part so far and so the products that I've suggested above are just educated guesses.

Your best bet is to go over our photos and measurements for our products and carefully compare them to the existing hardware in your window to verify that they match. You need to remove all the relevant parts from the window entirely so that you can be sure you aren't missing any important details. Using a functional, identical window elsewhere in your house is always a good idea. If the details differ in any way, tell me how and we can look into alternative options. 

If you're not comfortable purchasing these parts, taking the hardware out at this point in time, or if you have any doubts in general, then you may be better served by contacting a local professional who can do this project for you.