Water Supply Lines for Bathroom

I need to run water to the 2nd floor bathroom. Should I run 3/4" up from the basement and reduce down to 1/2" for my connections or just branch off of the 3/4" in the basement and run 1/2" up to the bathroom?

1/2" for hot and
3/4" for cold and then branch with 1/2"

so 1/2" for hot all the way up to the 2nd floor and 3/4" for cold up to the second then branch with 1/2"

That MIGHT be what I would do with copper, but not with PEX.

There's good and bad for going with smaller hot lines - unless you're running a recirc system, the smaller line means less waste while waiting for hot. But, 1/2" pex is closer to 3/8" copper in its ability to transport water. This may be okay for a single showerhead, toilet, or sink, but not for two at a time, or for filling a tub.

If you go with a manifold system in the bathroom, get one with at least one extra port and use it to run a return line should you want to add a recirculation system.