at 50ft, assuming a decent up-close view of a single person, you are talking a 16x zoom, at least (so usually a 20x or 22x optical zoom model). I used the calculator at PTZoptics to figure out field of view/zoom range
Fortunately, my budget is a little higher so we are looking at $2K for a 20x PTZ NDI model. For us, PTZ, not just a digital zoom, is a requirement. NDI costs a little more now (and does need some networking expertise to install/operate) but has benefit of being able to scale (add cameras in the future) with changing anything. Power over Ethernet, also means single cable to NDI camera. What I'd have liked to do is start with a camera and use USB then convert to NDI later. But the PTZOptics and Panasonic USB vs NDI models are different enough that I wasn't willing to compromise, so we'll spend a little extra now on NDI so we don't have to worry / deal with it later. Further, food for thought... we are getting a 1080p camera now. Assuming prices come down over time, I could easily see us moving the camera we buy now to alternate location and then get a 4K camera when donations and request justify such (and I don't expect to stream in 4K anytime soon, more for larger sensor better low light capability), and in case as a service we record something like a wedding and can capture that in 4K [though this is all more likely to be wishful thinking.. but who knows]
You can get cheaper cameras... but beware security cameras with low frame rates and really poor motion motors. Then there is the integration controls with OBS.. I was leaning towards PTZoptics, but have heard too many complaints about inconsistent color/quality, and a few other items, so likely to go with Panasonic at same price [and I can't ..at the moment, still researching.. justify the premium price of the Sony models.. which don't have features of Panasonic]. As this has to be able to run with volunteers, I'm prioritizing native English speaking support channels over lowest price [so avoiding some recent new vendors from Asia with inconsistent, to low/non, support response complaints]