The best soil for raised beds is indeed your own garden soil which has been amended for your optimal use. That is for whatever you are growing in the raised bed-will assume vegetables. If you have the cardboard layer there to prevent weed seeds from germinating and/or to kill the existing turf 6-8 weeks ago you can now pull up that layer and spread a 2-4 inch layer of compost over the area. Then mix and fill the raised bed with a blend of 50-75% topsoil and 25-50% compost (or alternatively 50% topsoil, 30% compost and 20% other organic matter like leaf mold or well-rotted manure) is recommended.
The best topsoil is characterized as loam having 2-10% organic matter so read the contents on the bags of soil. It is also possible to call local landscape suppliers for bulk topsoil.

Good resource information can be found at:
extension.umd.edu        (Soil to Fill Raised Beds) and
njaes.rutgers.edu        (Soil for Raised Beds)