This is partially copied for a previous answer.

The intestines absorb water mainly through diffusion. The epithelial cells set up a salt gradient with electrolytes such that there is a osmotic pressure for the water to enter and equalize the saltiness. Water mostly travels between the cells across the tight junction and makes its way to capillaries where it joins the blood stream. Some water will travel through cell but this is harder since it has to diffuse across the lipid bilateral.

Once water has entered the blood stream you have to consider how water can leave the body. Urination is the most obvious, but you also can lose water from sweating and respiration, breathing. The human body is about ~70% water by mass and the humans, as well as nearly all types of life, are very good at maintaining homeostasis, ie keeping the same temp, salinity, hydration, etc... Your kidneys play the largest role is how water is regulated. It can remove water from the blood supply and put it in the bladder and vice-versa. As you go through your day you will lose water through respiration and sweating and gain water through drinking. Excess water you eventually pee out along with some other waste products and excess salts. Urochrome is the waste product that makes your pee yellow. When you have a lot of excess water to pee out it dilute the urochrome and your will be lighter. If you have not drunk a lot then your pee will be more concentrated with urochrome and be a darker Amber color.

Urochrome is a breakdown product of heme, the chemical that binds iron in red blood cells and allows them the transport oxygen.

As for your question about priories for which body parts get water first I am not as sure. Water as liquid will spread out as needed going from high conc areas to low, except where physically prevented. However I am not entirely sure the question really makes sense, water is mostly used a transport vehicle and a solvent within the body. Water does not really get used in biochemical processes to a significant amount. Additionally water and all that it transports are circulated throughout the body via the circulatory system in vein and arteries.