One of the keys to optimizing good wheat grass/ barley grass is several fold.
Deep roots in deep soil.
Soil with effective micro-organisms present.
Soil with a wide array of minerals added. (Diluted ocean water will work)
Best if grown outdoors in natural sunlight.
The above not only ensures a nutrient rich grass but also will lessen the likelyhood of mold growth. Many confuse detox symptoms of poorly grown wheat grass for mold reactions.
Good wheat grass/barley grass will reap major health results.
The type of juicer you are describing will not extract minerals properly and will give high sugar. An auger type is better and a press is optimal.