Basically, forget "down". An aquatic species would need that even less than humans do. Most sci-fi ships have floors and are arranged into decks similar to naval vessels. An aquatic species would have little need of a floor, as they can float anywhere they need to be within the ship without anything to stand on or grab onto.
Now, Earth fish have a swim bladder, helping to provide neutral buoyancy, and in most fish the arrangement is most stable when there's a gravitational force on the fish, with the result that fish in zero-G tend to look uncoordinated and disoriented. We've done similar experiments with many other animals, including birds and cats on "vomit comets" for short periods of weightlessness, and the results are similar; zero-G is a very novel experience, and most animals don't know how to function without a downward force acting on them.
Humans are similar in this regard, but we have advantages of sentience; we can understand what we're about to do so it isn't a surprise like it is for a cat or a bird, and we can be taught to maneuver in zero-G without having to learn it from scratch. A sentient aquatic species, theoretically, would have a similar ability to "groupthink" and thus reduce the difficulties any individuals might have.
As far as the ship design, the biggest hurdle is going to be getting water out of the planet's gravity well. The Tsiolkovsky rocket equation models a fundamental truth of rockets; they have to lift their own fuel, at least what they haven't burned yet. As a result, achieving escape velocity from an Earth-like gravity well requires the rocket to be much, much more fuel than payload. "Payload" here is basically anything that isn't fuel, including the cargo vehicle but also the non-fuel part of the rocket system like its fuel tanks, pumps, exterior sheathing, nozzles, etc., which increases as the amount of fuel does, thus requiring either even more fuel or less "useful payload", what you actually want to put in space. Our engineers, therefore, endeavor to make everything they put into space as light as it can be, especially those parts of the vehicle that are disposable and used only to house the components of the rocket itself. We also figured out multi-stage rocketry; when the fuel in a stage is gone, you can lose the containment for that stage and save that weight on the next leg. Practically every manned spacecraft was launched on a multi-stage rocket, it's just been the only technically feasible way to do it.
As one example, the Space Shuttle, one of the most effective launch vehicle designs in human history, used an orbiter that weighed 100 tonnes (100,000 kg). Inside that orbiter, another 30 tonnes, max, could hitch a ride to LEO. The total maximum launchpad mass of the STS, including the external tank and boosters, was 2,000 tonnes. That means that using the Shuttle to get 30 tonnes of stuff into orbit that you plan on leaving there requires a system that is 98.5% "unusable payload". Even considering the orbiter vehicle itself as "useful payload", being the quarters for the crew and a good place to conduct zero-G experiments before the ISS was finished, the total launch vehicle is 93.5% fuel and fuel containment.
One last thing is shock dissipation. Water is classically an incompressible medium (theoretically its density can be changed with pressure, but the ratio of force to change in volume is many orders of magnitude more than for a gas). This is typically bad news for aquatic beings when a strong force changes the water pressure significantly. "Shooting fish in a barrel" turns out to be really easy, because the shock of the bullet entering the water is enough to stun or kill the fish swimming in it, similar to the effect of a flashbang in air; you don't have to hit them with the bullet (and in fact the bullet will slow to nonlethal velocity in the span of a few feet).