If you're not so "full of money", try a good open source engine such as "Ogre3D" or "Retribution Engine" for some good games...
If you have ample amounts of cash to play around with, try a full-on commercial engine such as "Unigine", "Gamebryo", "Unreal Engine 3"...
But if you have money but not THAT much, use Unity3D, it is good engine. It is built for Macs, and so can only be used on Macs, although if you get the professional edition, you can also create games on PCs.
Otherwise just use Ogre3D... I'm not that into game engines, but you'd want an engine that has good physics, graphics rendering, collision, high "modifiability" which I recommend Blender3D for... but if you're serious about developing but don't have much money and aren't gonna go with anything open source, then I would recommend Torque Game Engine Advanced (TGEA). Sure, it has a high learning curve, but from reviews its worth the learning...
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