LÖVE

Could anyone recommend a good place to get started with moving from designing simple 2d games to simple 3d games?
I understand its a lot more complicated but I'd like to start learning a bit about it, and I have no idea where to start.

Unity, Ogre, and the Unreal Development Kit (UDK) are notable free 3d game engines for hobbyists. You might want to start at their forums as they could probably better point you in the right direction.

I would also like to recommend Panda3D or the Blender game engine, if you want to stay cross-platform. I believe they both make use of Python for the scripting.

Unity is excellent. Ogre3d is more of a rendering engine than a full-featured game engine. Whatever you do, don't try to make your own 3D engine if you want to actually finish a game within the next 5 years.

I'll check them all out, cheers!