Question / Help Streaming IP Cameras with a Laptop

We're streaming our events from 8 IP cameras placed around the race track. We've borrowed a machine with an i5 6600k CPU and a very nice GPU (not sure what) for previous events. We want to invest in our own server for this season and because the kit has to be transported to each event, we would like to use a laptop to save space. Are we asking for a hard time by doing this? Are we better off getting a desktop?

Can someone make a recommendation about what sort of specs we need? We have just 10 scenes; the 8 cameras, an overlay of the live timing (browser) and sponsor logos that's overlaid on each camera scene and a scene for when nothing's going on showing the start line and some old videos from other events. No scenes have more than 5 objects. We want to stream reasonable quality 1080p at 30fps.

We don't have a huge budget, so I've been looking at used laptops on eBay. Will something like this be good enough?
https://www.ebay.co.uk/itm/PC-Speci...407483?hash=item1f0be2ed7b:g:RkoAAOSwW4JeU~0g
 
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