You don't need to download the apps again if they are already on your computer.
Try this:
Click on your iPhone in iTunes. In the main screen, you will see a bunch of tabs. Click on the one for Applications. At the top left of this screen, there is a button you can push to sync Apps. And then there will be a list of your Apps, and you can select which ones to sync to your iPhone. You can also set the layout of your iPhone screens on this page. once you have everything layed out the way you want it, just hit the Sync button on the bottom right. this will upload all of your Apps to the phone. Now - if you want to restore your App data from your backup, just do your restore again, and then your old App data should be loaded into your Apps.