How would you determine the best concentration of solutes to give a patient in need of fluids before you introduced the fluids into the patient's body?

You would consider the route of administration, for sure. Is the fluid going to be introduced orally? Through an IV line? Knowing the patient's current fluid and electrolyte levels in their blood would be highly helpful. If you put hypertonic solutions in the the body orally, water will be shifted from the circulatory system into the bowel. This may help someone with fluid overload in their blood to remove some of the water from their blood. It would also help to add water to the stool in the digestive system and act as a laxative. (Osmotic saline laxatives work in this manner. If you put hypertonic solutions in an IV you will pull fluids from the interstitial space between cells as well as from the bowels to the circulatory system. This would help reduce edema. If you put hypotonic solutions in the body orally, water will shift from the digestive system to the circulatory system (and will also dilute electrolytes in the circulatory system). This method may be used to reduce electrolyte concentrations in the blood, and to hydrate the circulatory system in general. If you put hypotonic solutions in an IV you would dilute electrolytes in the circulatory system and would shift fluid to the interstitial space between cells. Isotonic is probably the best way to go if you don't want to shift fluids or change electrolyte concentrations in the circulatory / digestive system. 0.9% saline would be an example of this, and is generally the most widely-used solution for basic rehydrating someone through an IV.

Small intestine because that is the organ which absorbs nutrients