The shutter speed issue is important, but it's also misunderstood.
Most of the professional aquarium photographers are not photographing fish in aquaria. They place the fish in tanks that are too short and too thin for the fish to move. Effectively the fish is wedged into place, which keeps it in the field of view. Sometimes, a pane of glass is placed in the tank, and the fish trapped between the glass and the front of the tank. Either way, the fish isn't able to move, so once you're in focus, you're pretty well guaranteed some good shots.
So trying to get "professional" pictures in a real aquarium is a bit fruitless, because the pros aren't able to do that, either. And yes, you're right, it's best to start with static fish like catfish, gobies, cichlids, and so on. Tetras, guppies, and other hyperactive species are much more difficult. In two years I haven't managed to take a decent portrait of a glassfish yet!
Shutter speed can be compensated for (to some degree) with light. A longer shutter speed compensates for a dark aquarium, but in the process, the fish moves out of focus. Or, just as annoying, other fish or air bubbles slide into view. A short shutter speed will solve the focus issue, but at the cost of a dark photo. You can use a flash, but then this bounces off the glass and messes up the picture. If you angle the camera, you can avoid this a bit, at the cost of losing focus on part of the frame, so the best approach is to get the tank as bright as possible, and then switch off the flash.
I wonder if your camera has automatic shutter speed or just the one shutter speed? That would make a difference in usage. If it's automatic, then contriving a situation where the camera "thinks" a short shutter speed is required might be the solution?
Cheers,
Neale