One consideration, although it might not have the look you were hoping for, is to use the rubber liner material for outdoor fish ponds. Basically you take it back far enough and high enough that there's no chance of the water running over the edges, then let your plants grow over it. You will also get a lot of moss/algae growing directly on the rubber. And they make a spray foam for ponds which is dyed black but is safe for fish (once it cures), you can use that to shape the banks of the spring. as it wanders through. Note that you could also use this spray foam to fully shape your waterways, then cover it with a coat of cement to seal it up water-tight.
In case you haven't thought about this aspect yet, one of the things you will need to consider is that your critters are going to knock dirt, sticks, and plants into the water, which will get washed downstream. You will want to have some way of filtering the water before it dumps into the aquatic pool or it will be muddy in a month. Note that there are a lot of plant roots that help pull minerals and contaminants out of the water, but it would have to be flowing really slowly to fully clear the water before it hits the final basin. It might be useful to have some standing pools along the way though, you can arrange it so heavier materials have a tendency to sink to the bottom of these pools which makes cleanup a lot easier.
Also do some reading on bog filters -- this is a technique where you have a heavily-planted area that the water flows through or percolates up through, and again the plant roots do the heavy cleaning, however this method will also trap the particulates. This technique is used on fish ponds for a completely natural filtration system with zero chemicals involved. I use a combination of this (huge growths of trailing plants, irises and grasses around the pond and stream) along with filters that promote beneficial bacterial growth to handle all of the filtration in my pond. Not only does it keep the water crystal clear, but the fish love nibbling at the roots.
Sounds like you have a huge project ahead of you! I'm curious how large you plan to make this in order to keep all the areas completely separate, keeping the excess humidity out of the desert section is probably going to be a challenge.
