What is a good third party battery box and receiver?
As you have mentioned, there is BuWizz and SBrick which, while primarily are intended to work with smartphones, are said to be able to work with joysticks or gamepads, albeit possibly with bugs.

I don't really see why would your age mean that you can't do modding, but assuming you have budget restrains or parents who would not allow it then these are valid reasons. Anyways, I'm sure you have your own reasons, just don't underestimate your abilities just because of your age.

There is of course the new Powered Up system from Lego, on the right side of this image you'll see the controller and the motors currently in use:

Drawback: There are no servo motors available for it yet, so you can't fully control the 4x4 crawler without extensive modifications to either


use a second motor for steering or 
settle for a tank-style drive with a separate channel and motor for the left and right wheels.


Another third party solution I have managed to find is the CADA controller. The main selling point is exactly what you are asking for:


  The most interesting feature is indeed dedicated controller, unlike buwizz/sbrick there is no need for smart phone.


According to one reviewer: 


  The range is limited to 10-12 meters


so it should yield better results as the PF infrared remote.