Pex is the best. Easy to flex, buryable, freeze proof, can run hot or cold water. The only real downside is the tool it takes to properly use fittings costs about a grand. There are other "homeowner" type fittings that are acceptable and that tool only costs a hundred or two.
Most people use PVC, as its the cheapest, real easy to work with, easy to modify/add fittings, etc, lots of parts available, did i mention cheap? You do have to bury it and/or insulate it good because it will crack if frozen with water in it, but its slightly more forgiving then copper, plus you can get it in more sizes.
Copper is probably the worst. Hard to work with, fragile to punctures, suseptible to freezing and bursting, doesnt bend.
Not ideal to share a tranch, code usually says they can share a trench if they are 12" apart. I'd put the water down lower, and one good idea with any
underground tubing, especially water supply or waste is wrap its length with a wire that sticks up at the beginning and end of the run, so its easy to locate later if you have to. Or if you want to go super budget, another neat trick is after you shade the pipe (thats where you bury the pipe you just ran in sand or dirt for a few inches so that once you finish burying the trench the bigger rocks dont puncture the pipe or create voids in the soil) run some one inch neon "tape", kind of like caution tape, on top of the shaded pipe just below the surface. That way if you or someone else is digging they will hit the tape first and not the pipe/wire.