I indent to proceed to the purchase of a 3D engine.
Which 3D engine do you propose?
Is OGRE A Game Engine?
No. OGRE can be (and indeed has been) used to make games, but OGRE is deliberately designed to provide just a world-class graphics solution;
Well, you asked for a 3D engine for games - a game engine is something completly different, like "rpg maker", "game maker", "mugen", etc - so I pointed you to a 3D engine;
'But there's no easy way - you have to test a lot of 3D engines to find one which will best suit your game/application. It could be Ogre, Irrlicht, Horde3D... anything. Just try out the engines, see how complex it is to write a simple demo of what you want, and see which gives you better results, not only in performance, but also in development time.