>Is having to learn a game engine going to be faster than starting from the ground up?
Yes, pretty much by definition, since a game engine saves you the time of writing an engine. ;)
Unity[0] and Game Maker[1] both come with tutorials which will show you how to build a basic game quickly. Game Maker uses its own properietary scripting language called GML, and Unity lets you do scripting in Javascript, C++, and Boo, which is basically Python. Also, attempts are being made to integrate Clojure support in Unity as well[2]
On the other hand, if you like actually writing the code, there's a good chance there's a low-level framework (like SDL[3] for C++) which will let you code, but still take care of some of the hassle of cross-platform support and graphics. I've only played around* with SDL and C++ but there are quite a few tutorials for it.
Also worth mentioning is Construct2[4], a game engine for html5/js. It is possible to do 3d rendering in javascript/html5[5], but as far as I know, only Chrome supports it well. Last I checked you have to change the config settings in firefox to allow opengl rendering to work and I just assume IE doesn't support it by default.
If you want to work with 3D and want to get something done then Unity might be a good idea, although of course you're going to need good models, etc. Game Maker supports 3d but it's primarily for 2d.
[0] http://unity3d.com/
[1] https://www.yoyogames.com/studio
[2] https://www.youtube.com/watch?v=tJr_TD1BtF0
[3] https://www.libsdl.org/download-2.0.php
[4] https://www.scirra.com/construct2
[5] http://www.ambiera.com/copperlicht/
*I've got some of the basics for Space Invaders done, and it's taken a while, after getting bogged down with creating a spritesheet manager and an entity component system, but I have a thing and it shoots bullets, and that's nice. John Carmack won't be taking my calls anytime soon.