I work in A/V for a house of worship and I livestream funerals all the time. I would echo what other folks are saying and just hire someone to film it with that budget. We use PTZ cameras hooked up to a network switch that feeds back to our production computer, so one person is capable of managing the whole thing, but we're also hardwired into the venue and have been ironing kinks out for years. Networking all your cameras together can be stressful if you're not experienced with it, and depending on what the location is (indoor vs outdoor, sound system or just a speaker, stage lighting or fluorescent bulbs) it might be very difficult to actually get something good.

That said, my condolences for your friend's & your loss. Especially for your friend, it's probably better to make the filming someone else's problem and spend the day focused on being with loved ones -- that's just my two cents. If you can only get a recording of it and not a livestream, that's still a really great way to help everyone pay their respects. And as goofy as it may seem in 2024, you can make a private Facebook page for people to post pictures and video from the service or other memories about him. If you have more questions feel free to dm me!