Centrifugal Juicer
A centrifugal juicer processes the fruits and vegetables with a shredder disc that spins at very high speeds. This is a popular type of juicer on the lower end of the cost scale and includes brands such as Breville, Juiceman, Jack Lalanne, etc. This model does very good on most items and ok on leafy greens. It does not do wheatgrass.
Recommendation is a Breville model.
Single Auger Juicer
This type of juicer operates by using a single auger and spins at a low speed (70-80 RPM). The lower RPMs help preserve nutrients and allows a longer potential juice storage time due to less heat, friction, and oxidation. These will juice anything including wheatgrass. Also does nut butter, frozen parfaits, and baby food.
Recommended models: any of the Omega 8000 series or Omega VERT 350.
Blender
Many "juicers" prefer a blender and consume the whole food (juice and fiber). Given the variety of fruits, vegetables, and the frequency you will use this, I highly recommend one of the higher end models such as the Vitamix or Blendtec. These models have around 2HPs and make quick work out of anything. I have a single auger juicer and a Vitamix and I use the Vitamix more. Since I have both, I like to juice leafy greens and then combine that juice with whole fruits in the Vitamix. That way I get whole food/fiber with the fruit, but not too much cellulose from all the leafy greens, which is much harder on the digestive system. Also, my diet is 80% fruit, which tilts the scales toward the Vitamix.
Recommendation: I picked the Vitamix, but the Blendtec is on par and also has a very loyal following.