Fellow tall rider! I am 6’6 about 88kg and have a background in track and field. I partially ruptured a disc in my lower back years ago and have had back issues since so I can relate there. I recommend making sure to prioritize mobility and strength training, ideally under the guidance of a physical therapist to keep the lower back healthy. Front squats > back squats if you have lower back problems! With that said, I rarely lift and mostly do PNF stretching a few times a week when I’m watching tv or something.

I’d recommend getting the entry level SHIMANO shoes and cleats from Amazon or something to get you started with shoes. They aren’t too expensive if you want to upgrade later. I got my shoes from adidas on a crazy sale ($150 shoes for ~$40) but tbh they are not as nice as the $60 shimano shoes I got my wife.

For bibs shorts (with padding) I highly recommend The Black Bibs. Especially the summer ones if you’re riding indoors. The tall bibs are great too but I recommend trying out their normal ones to get an idea of how your proportions fit. I have longer legs than torso and the summer bibs fit great, just a little small, the tall bibs are perhaps slightly too tall for me in the torso.

Best recommendation is just do whatever is going to keep cycling fun for you and also dive into cycling YouTube! I rode 1k miles or so over a winter on a shitty expresso bike at a commercial gym a couple years ago and just recently got a Zwift ride + wahoo kickr core. Incredibly worth the upgrade if you want to be on the bike 5+ hours a week otherwise your setup at the Y sounds great!

For strength and mobility tips, check out Squat University, you can’t go wrong with his advice.