I've kept track of my depths and times on all my dives. Not having a dive computer I always ask the Dm/guide at the end of the dives and write it down in my log.
These are always canned 2 tank dives so one assumes the DM knows the depths and times since they do them every day for cruise ship passengers. They also know the pressure groups and surface times and certifications of the divers.
In my experience of 26 dives they do a pretty good job of looking after you and profile the dives to the least experienced diver. 60 feet and 45 mins are the outside limits for dives. Unless there are a lot of divers in which case they will split the group based on experience and certifications. They are quite used to having inexperienced divers. In other words they pretty much hold your hand throughout the dives.
As for equipment, I have a wetsuit and a mask, I rent everything else. I'm not cruising/diving again until next January. I hope to have a dive computer by then as well.