This will work if everything you want to keep is on the iPad, or you've already got your iTunes library working on the new machine. If not, then you'll want to solve that problem first.
First, in iTunes on the computer, got to the Store menu and authorize the machine. Then go ahead and login to your iTunes account by clicking on the sign in link at the top right.
As a precaution, open preferences, go to the Devices tab, and turn off auto-syncing. This should prevent iTunes from syncing before your ready, and causing you to loose some content.
Now connect your iPad.
When you get the erase/sync dialog, there should also be a Transfer Purchases option. Choose that. If you do not get that option, cancel out of the dialog, right click on the iPad in he Devices list and choose Transfer Purchases. Alternately you can select Transfer Purchases from. . . under the File menu.
When it finishes (this may take quite a while, depending on how much stuff you have on the iPad) make sure all your stuff got transferred. If not try the Transfer Purchases option again. On rare occasions, or when it gets interrupted, not everything will get copied.
That should put an end to the dialog about erasing your iPad.
Now go through all the sync settings for the iPad in iTunes, and make sure they are set the way you want. Note that if you have been syncing photos into albums, and that the sync is turned off this will remove them from the iPad. If those pictures must be recovered because they are no where else you may want to hold of syncing the iPad until you recover them back to the computer. If you have other copies, or were syncing with iPhoto, then just set it how you want.
Be careful about how the apps get synced. If you accidentally delete an app from the iPad all the documents, settings, game progress, ect associated with that app will be deleted too. You can get the app back, but until you've done a back up you can't get that stuff back.
Come to think of it, now is a good time to do a backup. Right click on the iPad under the Devices list and choose Backup.
Now, go to where the backup file is stored and make a copy. Because syncing always does a backup, your first sync will overwrite this file and defeat the whole purpose of this backup, which is to make the iPad recoverable if your first sync messes things up. Here is a link on where you can find the backup file for various OS's. You'll find it under the About Syncing and Backups section:
iPad: About backups
Since you have a Mac, I'll just say Time Machine is your friend. You don't have to have it on all the time. I keep a calendar reminder to do a manual backup every two or three days, which is good enough for my needs.
When you have everything set the way you want, and have confirmed that all your media is in iTunes (on the computer), or safely duplicated elsewhere on the computer, go ahead and sync.
