Use a java.util.Properties file to save off the current state of the table model before you exit the app. When you load the app, load the settings from the properties file.
Properties props = new Properties(new FileInputStream("table.properties");
etc... I usually loop through the column headers saving off the setting. It creates the file when you do: props.save();
If you need sample code I got it. email me at firstname.lastname@example.org
You can use this to remember size, location and anything else you can assign to a variable and store as a string, like color and font too.