Hi CCinAK,
Welcome to the Apple Support Communities!
If you are only looking to get certain data off of your Time Machine backups you would not want to use Migration Assistant. You would instead enter the Time Machine menu and select the file(s) you would like to recover. Please use the following article for the steps needed and as a resource.
Mac Basics: Time Machine backs up your Mac
http://support.apple.com/kb/HT1427
Restoring specific files or folders
Choose Enter Time Machine from the Time Machine menu. The restore interface appears. You can literally see your windows as they appeared "back in time."
You can use the timeline on the right side of the window to reach a certain point back in time. The timeline shows the times of all backups on your backup drive. If you don’t know exactly when you deleted or changed a file, you can use the back arrow to let Time Machine automatically travel through time to show you when that folder last changed.
Note: Dates in pink indicate the data resides on your Time Machine backup device. Dates in white indicate the data resides on your Mac. In OS X Lion v10.7 and later, portable Macs include local snapshots.
You can also perform a Spotlight search from the Finder. Simply enter a search term in the Spotlight search field, and use the back arrow to have Time Machine search through your backups to find what you are looking for.
Before you restore a file, you can also use Quick Look to preview a file to make sure its the one you want. Highlight the file and press the Space Bar to bring up a quick look.
To restore, select the file/folder and click the "Restore" button. The file will automatically be copied to the desktop or appropriate folder. If the file you are restoring has another file in the same location with the same name, you will be prompted to choose which file to keep or keep both.
Have a great day,
Joe
