I was asking more for advice for a new shark diver. Since I don’t fully know what to expect with the different types of sharks I’m asking the question to people who have done them. Are lemons good to start with over tigers, hammers, bulls etc
I can only tell you my opinion, which won't be valid for everyone. My first sharks were Caribbean reef sharks and nurse sharks, a good way to start. Some reef sharks get pretty big, but most I've seen weren't so much. Unless you're spearing or handling speared fish, highly unlikely to be a problem.
When you want to 'move on up,' I don't recommend jumping to tiger sharks! Bull sharks in high viz. water where you're not spearing might not be problematic I suppose, but they have a reputation as potentially dangerous, and can get big, so not my vote for 'next.'
I chose
diving with sand tiger sharks on off-shore wrecks out of Morehead City, NC, to advance toward
diving with tiger sharks (and lemons) with Emerald Charters.
The NC dives weren't shark feeding and my lemon exposure with Emerald was, so I'm not sure how the lemons would behave without feeding/baiting. The sand tigers were like diving in a cow pasture; medium-large spooky looking animals with no interest in bothering me. The lemons were similar in size, some larger, and milled around us (again, baited/fed).
The bull sharks I dove with weren't nearly as large as they get, it was fed dives, and they were more stand-offish than the lemons. The only hammerheads I dove with were scalloped in the Galapagos, not the great hammerheads sometimes fed out of Jupiter, FL and the Bahamas.
My advice: start with reef, then visit sand tigers or lemons, or a destination where you're viewing hammerheads at a distance (e.g.: Galapagos, Cocos Island), before you get in the water with sharks with a rep. for periodically eating people (e.g.: especially tigers).