I have to say last summer when I did my first dives with SD.com, I had a lot of suprises. I was surprised that very few of the divers had snorkels attached to their masks...I'm still not comfortable with the idea, so I know my snorkel will stay on my mask for quite some time yet. I was also surprised that I was supposed to climb the ladder with my full set of gear, including fins. I'd done Cozumel and Caribbean diving prior to that and was used to "hand your fins up and then climb the ladder" and my Cozy diving included procedures to hand up your weight belt, fins and your BCD/tank, then climb the ladder. So it was different, but I learned to do it and it broadened my understanding of boat diving.
I stopped leaving the snorkel on my mask for most dives after the second or third time I dumped the air out of my BC at the beginning of a dive to discover while inhaling underwater that the object in my mouth wasn't actually my regulator but was instead my snorkel.
I do carry a foldable snorkel in my BC pocket which attaches to my mask via velcro (although it works poorly), and do have a "real" snorkel I break out if conditions warrant or if I'm actually snorkelling. On the surface, if it's calm, I'll often swim on my back, or if rough or I need/want to swim face down, I'll breath the remaining air in my tank off the regulator.
Getting on the boat, it generally depends. I'll usually keep mask on and reg in, taking fins off and putting them over my wrists vs handing them up depends on conditions and number of people near the ladder (am I likely to be jostled off the line/boat contact by other people and drift away? How difficult would it be for them to come and get me if I do?) Most of the time, I do fins on wrists. And I do try to signal ok after I get in and anytime I break the surface, even if I don't think anyone's looking my way (or if my navigation sucked and I have no idea where the boat with the people looking is.
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Cozumel's a little different. The dive op I use when I go to Cozumel uses 6-pack boats where the ladder is hung over the side. I'm a big guy, and often the first up (or at least, was with my air consumption last time I was down there). Me + all my gear hanging off the side of the boat with only the captain on board isn't the most stable arrangement, so I hand my gear up generally, keeping mask and usually fins. Other people do climb up in full-gear, though.
As a contrast, one of the dive boats I've been on up here has a christmas tree ladder, and given the swells often seen up here, I ain't taking off a single bit of equipment until I'm sitting at my spot.