My experience is in the natural gas business, not water or plumbing, so take this with a grain of salt.
I'd run polyethylene hands down and wouldn't even consider copper. Copper will last a long time in the ground, but will eventually rust through. Plastic doesn't rust. The PE gas line that I'm familier with comes in 500-foot rolls. You could buy a whole roll of PE and you'd have a 300-foot piece to go to the new water meter and 200-feet left over to run to your out building.
Besides the pipe, buy a 500-foot roll of tracer wire and put that in the ditch with the PE. Leave one end hanging loose in the meter pit and bring one end up to some sort of terminator at the house. That way anyone with a pipe locator will be able to find your water line in the future, so it won't get cut during fence installation, additional utility work, etc.
You think you're going to remember exactly where the ditchline was forever, but you don't. Been there....done that. 14 gauge tracer wire runs about 8 cents a foot right now...so you're not talking a big expense. It wouldn't be a horrible idea to keep about 5 feet of your new PE pipe and 2 stab couplings back somewhere as your "emergency repair kit" if it would get cut in the future.
I wouldn't sleeve the PE either. The biggest danger to your PE line once it's buried is someone digging into it with a backhoe, trencher, or posthole auger. A PVC sleeve won't protect you from any of those hazards. A tracer wire might if they bother to use it.
Phil