Links to gear mentioned:
Focusrite Scarlett 2i2 Audio Interface: https://amzn.to/3hoMjIt
HuddlecamHD 94 Webcam: https://amzn.to/3aOtUDF
Hosa 5 Foot TRS to TRS Dual Patch Cable: https://amzn.to/30mNJvj
Neewer Tripod: https://amzn.to/34Dc826

I put together a cheap live stream setup for our church using mostly old analogue gear. I routed audio from the sound board mixer to an audio interface using a spare set of main outputs. It's a super low maintenance way to get decent sound without having to setup a separate mix. For video I used the HuddleCamHD webcam and boom we had a great looking feed for our online servicesall for about $300.