48 year old lessons 1st time lessons - help with what makes a good teacher

I've done some reading in this group trying to find answers to this question, but I didn't find anything that was specifically addressing what I'm looking for.

I'm looking to take western riding lessons for the first time at age 48 (with a badly arthritic knee - if that's relevant at all). A lot of the places around here (OKC area) don't really explain what qualifies them to give lessons. I don't know anything about horses, but it seems to me that simply riding most of your life doesn't mean you're able to give lessons right?

How do I know the instructor actually knows the right things to do and is teaching me correctly? What kind of qualifications should I look for?

One thing I see a lot of sites saying is the lesson is 1 hour but it's basically 30 minutes in the saddle. I don't want half my lesson time to be used for tacking up and grooming. I want to pay for an hour of learning to ride a horse. Obviously, at the beginning, I understand the need to learn those things, but certainly, after a few weeks, I'll be able to tack up my horse and put it away after the lesson without counting that as lesson time. I am unwilling to spend my money on an hour-long lesson that doesn't actually last for an hour riding the horse. Am I out of line with that expectation?

What other things should I consider when hiring a teacher? I have seen several posts here about looking for clean barns and healthy horses, but what else? I don't even know what I don't know :)

PS making an edit to say...

I'm not sure if people just aren't reading everything I said, or if I was unclear. At no point have I said I don't think I should learn how to tack and groom a horse. I think that's super important. My point was a lot of these websites say that lesson time is 30 mins of riding. They arent saying "that's just for beginners" or "for the first few months."

I 100% think that teaching me to put on tack and groom a horse should be included in lessons - just not forever. At some point, I should be competent enough with doing those things that it shouldn't be included in lesson time. Or at least that's how I currently see things.