I wouldn't use PVC or pex for that kind of water run, I'd use polyethylene plastic pipe like they use for wells. I ran 200' of it out to my barn, used 1". It's also a lot cheaper than either PVC or pex. They make it in 100psi rating, but I'd buy the 200psi, the wall is thicker and gives you better protection against rocks and damage. It comes in long rolls so you can run it without having any joints except at the end. If I had it to do over I'd throw a second pipe in the trench, it's so cheap compared to the labor that if you ever have a leak, just switch to the other pipe.
For the gas they make a special flexible pipe that you can use, it's yellow around here, not sure if that's standard or not. All the other advice is correct, figure out what appliances you're going to be running before sizing the pipe. Also check your gas meter to make sure it can deliver the extra load. People often have to change their meter when they buy backup generators because they require so much flow, for example. I'd at least think about hiring someone to do the design on the system, even if you still want to do it yourself. The gas company will provide some help around here sizing the meter, not sure where you live.