When we were first getting into space, we started with very fast, high-flying aircraft. Look at the X series of rocket-powered aircraft used by NASA to test all sorts of things related to space travel. For us, it was a logical step to first be able to get into the air, and then get into space from there.
For an underwater species, there would be a third step. Their first phase would be to get out of the water. Once they had the technology to be able to handle working out of their natural habitat, they would have to figure out how to get into the air. THEN would come the leap to space.
Given that, it seems logical that the best place to launch a spacecraft for them would be a large floating platform near the equator. The platform would give them access to the air, so any space ship would not have to deal with water, air, AND space, but only two of the three mediums. The equator is good because of the bulge of the planet and our rotation, on earth, it gives a significant fuel savings to launch as close to the equator as possible.
Rockets are not implausible. In fact, it seems possible that they might develop rockets before they ever worked out advanced aerodynamic theory. This is because you can create a very simple, primitive rocket by using water trapped in a container that can be heated, forced to expand, and provide thrust. If the species had a reliable source of portable heat, they may have developed the basic principles of the rocket engine long before even being able to build a platform on the surface of the ocean.
Water based species have plenty of access to hydrogen if they can generate electricity (separate it out of the water). That is a staple of rocket fuel for us. This all seems to point toward a space program that runs in parallel with our own, at least in general.
I am not convinced that they would necessarily put the pieces together the same way though. We had hundreds of years of experimentation with ballistics and aerodynamics (mostly for warfare) under our belt before the invention of the rocket motor. We had a darn good reason to try to develop flying bombs that could self-propel and drop on our enemies many miles away. The military incentive to develop rockets was critical to the entire space effort, from the "buzzbombs" of WWII to the ICBMs that provided the foundational technology for the lunar launch. An aquatic species would have a long history of under water warfare, but apart from using the surface to scout or spy on their enemies, what experience would they have with trying to lob missiles through the air? Why even develop artillery on the surface if your enemy's base of operations is the bottom of the ocean?
Necessity is the mother of invention, which means that I bet these guys would be considerably MORE advanced than we were before they actually put all the pieces at their disposal together and built a rocket capable of putting them into orbit. (Remember the motives for us to be in space even now: spying on enemies ON LAND -satellites aren't very good at seeing anything on the bottom of the ocean, which is what they are most concerned about). Ironically, they might develop this kind of technology as a reverse to our own nuclear subs. We keep submarines full of ICBMs under the water because it makes them easy to hide, so we know that no enemy can possibly take out all of them at once. Maybe they want to get into orbit (or the air) for the same reason? Hide their nukes from their opposing nations because nobody pays any attention to whatever is flying around in the sky or orbit.