Live streaming has very little to do with the processor, either family is overkill for that.
Otherwise it's a standard PC build with a little consideration for which gaming video card fits the budget, a PSU and case airflow that can handle it.
Not sure where to start, prices vary a lot based on your friend's location, how much of a rush there is to built it, whether there is a willingness to do rebates and/or look around a few times for sale prices. The latter two can easily shave 30% or more off of prices except for CPU and memory.
Does he have a case and/or PSU he would reuse? Too many variables! I think one of the other recent topics about building a gaming PC will handle the question since the only difference is the streaming aspect which isn't really demanding, just get something with gigabit ethernet and use that for networking, though you might want to put a 2nd storage volume, HDD in it to offload the bulk I/O from an SSD used for OS and as much as possible the gaming... and yet, it might be an idea for a later upgrade, not something to start taking funds away from the video card budget to do.