I think the Germans would have used the LSSAH and Das Reich Panzer Divisions for starters. The Fallschirmjagers would be used to capture key positions and gain ground for the Infantry.

The Luftwaffe would be used to keep a carpet of planes in the air, strafing bombings etc.

I would also see they would use at least 1 Gebirgsjager Division, sort of like a special forces type unit.

The Grossdeutschland Panzer units, since they were very elite.

The Kriegsmarine surface fleets, as a mobile artillery force.