I guess he is going to play Xbox games directly on the PC just with a console controller?
If so, a capture card will be useless. Software handles that in a PC.
If you wanna use capture cards, you will need an entire second PC using it to encode. That wouldn't be cost efficient, and only like 1% of streamers do that, since highend consumer CPU's can handle 1080p@60fps encoding.
I guess we are talking about streaming on twitch.
Whats gonna limit him is if his not partner, So viewers can adjust the quality themselves. Since not all will be able to handle like 3500+ bitrate that the majority of stream has for source quality.
like 2000-2500 maximum bitrate is advised so the majority will be able to watch the video without buffering.
A I5 CPU would be sufficent for the 1500-2000 bitrate, which will be fine for 720@30fps for a none partner.
But I do recommend an I7 to be future proof for higher quality streaming like 1080p@60fps
And wired Ethernet is really preferred for gaming, specially for stream, because of the latency and frequency interference from other 2,4GHz signals. 5GHz have way more channels, but the router can't be to far away, since the range is considerably smaller.
tl;dr
No capture card, software will handle it.
I5 sufficient for mid range streaming, but i7 is recommend for high quality streaming.
Wired ethernet is highly recommend. Will add a wireless card tho.
This will take your above an beyond for 1080p or 1440p gaming, streaming 1080p@60fps. Without worrying any bottleneck on FPS or encoding. And wouldn't be needed to be upgraded for years to come.
http://pcpartpicker.com/list/dzCgnn - $1338.17
This will be sufficient for current use 1080p gaming, streaming 720p. Will need upgrades sooner.
http://pcpartpicker.com/list/khGVFd - $971.16
Windows 10 under 30$
https://www.kinguin.net/category/19429/windows-10-professional-oem-key/