1/2 " should be enough to run two fixtures simultaneously, sink and shower, if there is any possibility that there could be three in use, sink shower and bath, then i would run the 3/4.

Cold should be 3/4 because it has the added load of a toilet(you didn't mention it, but i assume you have one ), and because there is no advantage to running 1/2" .

From your comment on city inspectors, i assume you live in Texas??? finest government money can buy!

Regardless of permits or inspectors, you should check the plumbing code whenever possible. The majority of the code is based on a compilation of cut and try. it is what has worked in the past.
The problem with the code is that every house is different. It is not unusual to have to go beyond minimum code requirements to get satisfactory preformance. a house can pass code inspection and still have serious plumbing problems. But the code is a place to start. I wouldn't go below code minimums except in very unusual circumstances.

: : I am running copper water lines from basement to 2nd floor bath. Book suggests 3/4 copper hot and cold up with 1/2 branchs at fixtures, prohardware guys said use 3/4 for cold, but run 1/2 up for hot. Any problems here?, I understand that this will help with hot water demand as the service is for 1 sink, a bath, and a shower. Is there any potential code violations for this setup, I don't want problems later, no permits pulled as I have little faith in the city that approved the mess as ok when I moved in even though the kitchen sink was hooked to the gutter!