Sharks are difficult to keep because they require good water conditions, while they put a pretty sizeable bioload on the tank. They also require a very large tank, opinions on exact sizes vary, but the smallest shark usually commands at least a 240 gallon, with most sharks, especially those that hatch from an egg, require more then 400 gallon tanks. Also, they can typically only be kept with certain tankmates. They can get picked on by some fish, angels, triggers, puffers, etc, and any fish too small is at risk of being eaten.
Definitely can have live rock, just as long as it doesn't impede on room for the shark.
On the contrary, most small, as in newly hatched, babies, shouldn't be kept in large tanks. They will require intensive feeding, as they will be pretty reluctant to start eating. Something along the lines of a 40gal breeder or 75gal is about perfect. Nice and easy to spot feed. However the growth rates are pretty impressive, and within a few months, especially once they start eating strong, they will need their large tanks. However given the timely process it is to setup a large tank, it better be set up and running before you get a shark, because of the short timeframe. A newly established tank will not be able to handle the bioload of a shark.
Hatching a shark can be very rewarding and at the same time very frustating job. I think saying only 40% of hatched sharks make it, is generous. Also, the smallest shark, a Coral Cat, is usually only avaiable as adult. Bamboo's, Eppies, and Horn's are the ones commonly available as an egg, however as I said above, they grow to be much larger. Baby sharks require daliy spots feedings, as well as a willing fishkeeper to try a ton of different foods till they find something the shark will eat.