As per Joshua's answer, start with the three core books. With those, any basic campaign will open up to you.
To start a new campaign, you have a few options.
1: Build your own.
Building your own campaign can be quite rewarding, but also quite challenging. There are plenty of guides, both on this site and on the web abroad. Look for them and learn how to create an adventure of your own for 4.0.
2: Find/Buy a module
Campaign modules are basically new adventures that you can run. Some are available online (Look for 4.0 modules), and some can be bought.
3: Get an experienced DM
If you want an adventure but aren't sure where to start yourself, find someone who is experienced with 4.0 to run a campaign for you. DMs are looking for players all the time, and they'd be happy to lead you through a campaign, maybe even teach you the ins and outs of advanced DMing. Just make sure your group is okay with the DM you pick.
New books that expand the game and offer additional classes/rules/etc. can also help your game grow. But these three suggestions will get you started on a new campaign.