Here's how to do both. First, add a forwarding address in Gmail. Go to settings by clicking the gear icon and choosing Settings.
Click the "Forwarding and POP/IMAP" and choose "Add a forwarding address".
Once you've added the email address, a verification message will be sent to the email address you've added. Click the link in the email to verify the new address.
To FORWARD ALL EMAILS, go back to Settings --> Forwarding and select "Forward a copy of incoming mail to". You can choose how to deal with the original emails (best choice is to either keep in the Inbox or to mark copy as read). Click "save changes" and you're done!
If you want to just forward certain emails, you can set up a filter. Click on "create a filter" from the Forwarding tab, or go directly to the Filters tab to do the same. You can filter emails based on criteria like sender, content or subject line.
Once you've chosen your filter criteria, you can specify what to do with emails that meet those criteria. For this purpose, choose "forward it to" and then select the email address you've added. You can also use this same feature for other actions (like starring emails from specific people or automatically archiving emails on a certain topic).