Hi Saima,
First and foremost, I generally don't recommend duplicating the information in a relational database. If you plan to keep the fields continuously in sync, you will likely need to code a plug-in to do this. (e.g. if the industry changes on the Account, update all Contacts related to the Account).
But if you must duplicate this information, you are on the right track with the Global Option Set for industry. You also want to make sure that you are mapping the option set from the Account to the Contact such that new contacts will have the same industry when a Contact is created from an Account.
You can also make sure the workflow Jason described to on create of a Contact in case the user does not create the contact from the Account (such as through the Outlook integration). But you will need a plug-in or custom workflow extension to keep the duplicated industries up-to-date.