Game design

Hi Dilshad , If you want to be professional animation artist , 1st you should concentrate on acting skills , then 2D sketching, then traditional animation , as a common 3D software you can learn Maya or Max , if you know any of this 2 software , easily you can upgrade your skills to softimage xsi or any other animation software, at the same time if you want to build a career in 2D animation , then you should try learning flash animation .
As you said you want to learn game design , its again splited in two parts , one is the interaction part , which is normally taken care by the scripts and programmers and the other part is game artist , where you should have sound knowledge of 3D modeling texturing lighting and map extractions. For that you may learn 3D Maya or Max & for high end detailing z-brush , mud box etc.
Hope you got some idea .
Thanks .