I assume you mean camera work and forgetting things like gaming (at least on the same machine).
I do DJ live streams like this one. Two cameras and an overlay, plus a sound card coming from my DJ equipment.
Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube.
youtu.be
Ideally you want to find a laptop in that price range that has an Nvidia NVENC encoder so that it can take the encoding load away from the CPU (meaning you can give your viewers a better experience, and do more on the computer).
I'm running a:
THINKPAD W540 8gb RAM 2.5ghz i5 Quad Core with Nvidia K1100m graphics - just with an old hard drive in it.
But it's the Nvidia K1100m I bought it for. I'm not gaming - but I understand the benefit of these chips are amazing.
If you want to find out what to buy, used, in your price range, go and find out what 2012, 2013, 2014, 2015 laptops have NVENC encoders in them, and do a search. You may spend less than 400, I spent 250 on mine with some cheeky bids on ebay (as these are ultimately quite old laoptops!)
You will then need to go on youtube and search:
"how to optimise windows 10 for gaming"
"how to optimise windows 10 for streaming"
Follow all of their instructions.
And when you get it working, search:
"How to turn off all windows updates for gaming" and do that stuff or face the consequences of windows updates killing your perfectly fine streaming computer in the dead of the night like a thief of happiness.
(said, exasperated after months of messing around)
enjoy your streaming!