Does anyone here know about universal streaming devices? Or even just really good ones for a low budget?

My boyfriend is starting up a YouTube/Twitch channel and I'm trying to help him out with everything. I've gotten him a Razer headset, some other little helpful things, and the Elgato, but I want to move up from the Elgato soon.

So yeah,
I want to get some nice things within the nearish future. We collectively own a Xbox 360, PS3, PS4, Wii, Wii U, 3DS/XL, (Gamecube but I doubt there's an option for this??), two laptops, and one Chromebook. So like, halp pls.