First of all you need some way to transport things, paint and water just can't be easily carried. If you have a cart great or check to see if there is an extra AV cart in the library or I have even used a wagon (like a Radio Flyer, I like the one made
for off-roading with fat air filled tires).
I use liquid watercolors, but the procedures would be the same with pan watercolors. I try to prep 8 sets of everything I use, this seems to be enough for any of the classrooms I go to. I carry 2, five gallon buckets with me, one for clean water and one for dirty. I fill the clean about 1/3 of the way. I also have half sheets of poster board I use for place mats.
When we paint I have students pick up supplies cafeteria style from my cart or an available table. They get their paper, paint shirt, place mat, and brush. I pass out water cups and paint when everyone is settled, this avoids spills. if it is a rather messy group, or a teacher has complained about messes, I keep the paint and water cups in an old cookie sheet, a paper box lid, pop can trays or a shoe box lid to contain spills and drips. Once paint is out they have to raise hands to get supplies, this limits movement in tight spaces. I make sure to have paper towels cut in quarters available for minor wipe ups.
When we are done painting, place mats and paintings go on the drying rack. I collect paint and water cups with paint brushes in them. The dirty water goes in the dirty bucket and I rinse the brushes in some fresh water or leave them in fresh water to clean later, depending on how dirty they are, or if I have another class painting that day. I put a little clean water in each cup, swirl around and dump in the dirty before stacking them.
While I take care of brushes and cups, students put away all other supplies and wipe desks with baby wipes or damp paper towels. I start training them with this in Kndg, and they are pretty self sufficient by the 1st grade. If it is a messy hand type of day, I give them either wipes to clean hands or we go to the bathroom for a 30 second wash (our bathrooms have 8 sinks).
My goals are... easy to store, fast/easy to clean up and compact. This isn't the same system I use when I have a classroom. Then I try to have students take more ownership and be responsible for most set up and tear down.