If you add up all the the breakers in your main panel, they will exceed the rating of the main panel. The idea is that you will not run every circuit at once. The same principle applies to the sub panel in your shop.
For a shop, consider all the stuff that can possibly be on at once, say dust collector, lathe, lights, compressor, a powered hand tool and maybe an electric heater. You will find that's way under the rating of the sub panel.
Add 50% to that at least and run 220V from your main breaker with at least that rating on the wiring, with a two pole breaker to match that wire. So you may have a 50A breaker in your main panel which can shut down the sub panel in the shop. The fact that your shop panel is rated higher is irrelevant.
Your lights should be on their own breaker, that way if one of your tools trips its breaker, you are not in the dark while the tool spins down. Ideally each major tool will be on its own breaker, but in reality you might not achieve that. For example, my band saw and drill press share a breaker.
You should endeavor to load balance the two legs, so your 110V lathe might be on one leg of the 220V input while the 110V dust collector might be on another.
