If you don't have a Google apps account you'll need to use a utility to sync your Gmail calendar and contacts to Outlook.
To configure Gmail accounts for POP3, use Incoming mail server: pop.Outgoing server name (SMTP): smtp.Use the following settings for IMAP: Incoming server name: imap.Outgoing server name (SMTP): smtp.Use your full Gmail address, including @or @your_as the username.
In Outlook 2013 (and newer), Gmail uses the Sent folder on the server.
This folder is automatically subscribed to your IMAP account; expand the [Gmail] folder to find the Sent folder.
Beginning with Outlook 2013, you cannot choose the Sent folder; Outlook asks the IMAP server which folder it should use.
If the server supports XLIST or enhanced-list, or Outlook can match a folder on the server to it's folders by name, sent items will be stored in the Sent folder on the server, otherwise they will be in the local Sent Items folder.