Fascinating thought experiment!
Based on our current planet, if Earth's surface was completely covered in water, it would need to be at least 29,000 feet higher than today to cover Mount Everest, the highest point above sea level. Current sea level is on average only 12,000 feet deep, with the Marianas Trench, the deepest point in the ocean, only reaching 26,000 feet. That means our oceans would more than double in depth, completely changing everything about ocean circulation, sea life habitability, nutrient sources, oxygen production, and so much more. Likely, most of the ocean organisms would not be able to survive this scenario unless it happened on an evolutionary timescale (think millions of years).
Further, all the land and freshwater organisms would also go extinct: most plants, birds, mammals, reptiles, amphibians, insects, etc. This would completely change the planet's ability to support life.
If humans somehow survived, the number one concern would be producing drinkable water. We cannot live by drinking salt water, so it seems unlikely that any human survivors would live in any artificial floating city or ship without large-scale desalination infrastructure. In fact, any large population of humans would be dependent on resources and technology we do not fully have developed today for supporting more than very small groups of people. And those resources would likely run out quickly, as there would be no way to continue producing new resources without trips to the bottom of the ocean and building factories on the water.
The positive to your scenario is that it is very unlikely that Earth could ever be completely covered in water. Currently, 71% of the planet is already covered in water. And the only way to raise sea level would be to melt all the ice trapped on the continents (think Antarctica, Greenland, and mountain glaciers). If all the ice was melted and drained into the oceans, and we ignore any other planetary responses that would offset sea level rise, that would only lead to a maximum of 250 feet of sea level rise. This would flood all modern coastal areas and many really low-lying areas (like Florida and northern Europe), but the interior of the continents would remain mostly unaffected.
If the world were to be covered by water (let's hope it does not happen), it would happen over a long time scale, so human will have time to develop necessary technology and adapt to the "new life style". I think the best option for human would be to build large floating islands from all the plastic waste that people are creating right now. These islands need to be large enough so they are stable against ocean wave. Sufficient size is also necessary for a stable ecosystem in order to produce enough food. Well, this is not ideal, but it seems easier than moving everyone to another planet.
If Earth were covered with water, we would all have to live on boats or floating islands like the Uru people. The Uru live on islands that they make islands out of reeds in Lake Titicaca, which is on the border of Peru and Bolivia. We would only be able to eat fish and seaweed, which we could either catch or grow in floating pens, which is a form of aquaculture.
If the water were deep enough, we would not have to worry about tsunamis, because tsunami waves only rise up high on coasts where the water is shallow. On the other hand, hurricanes would be more dangerous, because we would not be able to go inland to avoid them. However, even if all of the ice on Earth melted, it would not be enough to cover all of the land. The International Panel on Climate Change has predicted that global average sea levels may rise by about 0.26 meters to 0.98 meters (0.8 - 3.2 ft) during the 21st century. This would result in lots of flooding, but would not cover everything.