I think that the diving is very easy off of Cayman Brac and Little Cayman. All the dives are moored boats dives, the walls start pretty shallow, and there usually isn't much current. you have the option to follow the dive guide or go off on your own. Of course, you can always run into bad weather and rough seas anywhere you go, but in general the Caymans are very easy diving - and also some of the best diving in the Caribbean IMO. You will have short boat rides to the reefs, especially on Cayman Brac. The boat trips are a little longer on Little Cayman but the diving is even better. As new divers I don't think you would be disappointed with either location - but you may become spoiled!
And if you stay at the small, diver-dedicated, all-inclusive Cayman Brac Beach Resort or Little Cayman Beach Resort then you will dive with Reef Divers - which is an excellent dive op that provides full valet service as part of their regular service. So there will be no lugging of heavy equipment and you only have to rinse and hang your mask, fins, snorkel, and wet suit after diving. It couldn't be easier.
You will have to fly to Grand Cayman and then take Cayman Air to the sister islands of either Cayman Brac or Little Cayman. I am guessing but I think that from Utah you might have to fly to someplace like Miami and then to Grand Cayman before taking the hop over to CB or LC.
If you prefer a more developed location with restaurants, nightlife, shopping, and lots of topside activities, then Grand Cayman is a good choice - and it is a shorter flight. I prefer the diving in the sister islands but there is some great diving around Grand Cayman. The Cobalt Coast resort on GC was recently bought by the same family that owns CBBR and LCBR and Reef Divers has been the in-house dive op since Dec 1 and they offer valet services there, too.
You don't have to worry about drinking the water or eating the food on any of the Cayman islands.
Have fun wherever you go!