If I were the OP and I didn't want to use low level directx or openGL, then I would use either Irrlicht, or Ogre3d to do my drawing/window manager, and input ( ogre3d comes with an input lib, irrlicht handles this too ).
Irrlicht is easier to use and get started, Ogre3D is more tweakable.
However I would rather use low level openGL and libs like GLFW, GLEW, and GLM.
If you're still checking out new engines I suggest Platinum Arts Sandbox. it's open source and written in c++, so once you're a c++ wizard you can rewrite the code, change physics and make it into the best game engine in the world (for your needs). the scripting langue is a full fledged programming language called Cubescript. It's not the best language for beginners due to the lack of documentation but if youre into c++ i bet you can pick it up just fine. Looking at the c++ source code gives you a great idea of the programming that goes into a 3d engine. The licence is very generous as well. I hope this helped.
Learning a new framework for programming like C#(Unity) and Unrealscript(UE3) is definitely not a good way to start. UE3 and UE4 does allow you to code c++ directly for your needs but it requires you to purchase the full license which is very pricey for us indie developers. If you really want to stick to c++ coding, i advise you use Cryengine. CryEngine and UE3 is definitely the best choice among the other engines said here. But if you want to try UE3, you would find it easy to learn most especially Unrealscript is based on common C++ syntax. However, you could write your own engine, but it requires you alot of effort and time to finish it. It'll take you years to even finalize a beta version of your engine that is stable enough to create a simple game. I chose UE3 because it's really easy to learn. If you are a C++ programmer, you can just start on class structures in UnrealScript and go start programmming.
