Blender ISN"T a game engine, its a full software package like Ivy said, but it DOES have a built in game engine. If nothing else its free and more than sufficient so far as your modeling/sculpting/texturing needs would go. Max and Zbrush aren't in the least bit necessary, and I wouldn't even consider them unless you've got long term plans to be doing a lot more of this kind of thing and/or have money to burn.

CryEngine would be overkill for your needs I think, as would the Unreal engine. I would consider Unity3D, its a fairly robust game engine, and has a free version available. Blender's internal game engine might be able to handle what you want [I'm not terribly familiar with it] if not, Unity should be sufficient for your needs.

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Lightwave | Blender | Marmoset | GIMP | Krita