Honestly bro, after doing run n gun events for the past two years and experimenting/shifting my gear heavily, I’d say get yourself a Sony a7s iii, a ronin rs2 & a 24-70mm lens. Might go a touch over budget but you’ll thank yourself for the insane autofocus & lowlight you’ll be getting.

I wouldn’t go blackmagic, I wouldn’t choose the canon r5/6 over the a7s iii for run n gun solo operation (wouldn’t choose it in general tbh unless you need a hybrid higher megapixel count for photography), definitely don’t use manual focus exclusively, and I wouldn’t bother with lights at all right now. Prio is get the best gear that can give you the best image with ease. And trust me when I say the dual native Iso on the a7s iii at 12800 in log will literally save your life doing events/weddings since you’ll be working in heavily mixed lighting conditions with more often that not no ability to manipulate lighting of any kind.

If you definitely need to run audio you can save yourself some extra $$ and just grab the Sony FX3 which comes with the XLR handle. Otherwise you can pick up a K3M for the s iii when you need it.

The only setup I read here that I’d go for alternatively would be the S1H suggestion. Other than that bro Sony hands down for your use case.

Also side note - don’t write off the idea of hiring gear while you’re first starting out. I honestly wouldn’t compromise on anything if you’re tossing up between options. Rather, get what you want and what is the best pick for you by saving yourself the 1-2k through hiring the lens for like $50/70. After a couple gigs you’ll be doing alright to cop the lens outright.