You cannot create favorite table templates in AppResponse version 9 and below.
What you can do is indeed have projects with the tables you want saved in it as you are describing.
Alternatively you can create a custom insight that represents a favorite table with the columns that you want.
If you haven't created insights before look at the documentation to launch the Insight Developpment Kit, you can select graphical elements: a "favorite table" here:
Configure the table by double clicking in it and choose the columns you want
Then add it to the insight layout:
Test the layout to adjust the size. Save it to you local insight directory ( specified in the preferences ) or upload it to the appliance and you will have an insight "table" the way you want:
That way you do not have to re-open a different project just for that custom table.
Also keep in mind in AppResponse 11 you can save your customized favorite tables.