Look for a (good!) gaming PC. Gaming specs and live-media specs are often very similar if not identical. Make sure the GPU can ENcode video; not all of them can.
You'll have to source your own capture card. No gaming rig comes with that. I like these:
Acasis PCIe capture card supports multiple HD resolutions (such as 4K60Hz), bringing crystal-clear visual effects to the audience. It also supports quad HDMI or SDI simultaneous input, allowing you to flexibly adjust between different camera angles or input devices. Solve your professional video...
www.acasis.com
PCIE CAPTURE CARD AC-4HDMI (Quad HDMI-1080P60).zip AC-4SDI (Quad SDI-1080P60).zip AC-4HDMI PLUS (Quad HDMI-1080P60).zip AC-4SDI PLUS (Quad SDI-1080P60).zip AC-VS2583 (2 HDMI-4K60).zip AC-VS2584 (1HDMI+1SDI-1080P60).zip AC-VS007 (Dual HDMI-1080P60).zip AC-VS014 (2HDMI+2SDI-1080P60).zip AC-VS049...
www.acasis.com
For audio, do it outside of OBS, so that OBS can have exactly one audio source at all, and that's the final, finished soundtrack to pass through unchanged.
Get a good mixer that can also master it for broadcast, and not just add sources together and spit out their sum. You can do that with a digital console - I like Behringer's X32 and XR18 - or you can do it with an analog console AND an analog compressor that you plug into it.
However you do it, you want to have your final soundtrack right up next to full-scale without ever going over. And because this is live and you don't know what's coming, it's the compressor's job to tame whatever peaks there might be, so that you can put it there safely.
Bad settings for that compressor are of course audible and jarring, but good settings are practically transparent, while keeping things well-behaved. It doesn't really matter what compressor you use, as long as it has enough adjustment to give it some good settings. The channel/bus compressor on a digital console is usually enough, as is the now-classic Alesis 3630 analog compressor, or anything else that has similar settings.
Or you can do it in a DAW on the same machine as OBS. (Digital Audio Workstation) That's effectively a complete sound studio all in one app. But if you can afford to have a separate control surface like a physical console has, that's probably better. Although, there *are* control surfaces that can control a DAW, so that might also be an option.