Exactly how useful is "lucky" anyways? Would a Rich Home World or other
benefit be better than avoiding random galactic disasters (and the occasional Antaren fleet)?
Lucky isn't very useful. Disasters don't happen very often, and the dangerous ones can be dealt with. If the star in one of your systems starts to go supernova, set all the colonists there to research and it will fix itself in ten turns or so. If you get pirates, just station a fleet in the system and kill them. Space dragons, eels, crystalline entities...whatever the problem is there are usually solutions that don't require you to spend racial picks. As to the antarens...they usually go to whomever is most powerful. If that's you, just kill them. All lucky really does for you that can't do on your own is prevent planets from being overworked and losing one rating of mineral deposits. And every now and then you'll get an upgrade, a population boom, or a diplomatic marriage...but these things happen so infrequently that it's barely worth one pick, let alone three.
Aquatic
Aquatic is a decent, but not usually spectacular pick. It's situational depending on your galaxy parameters at the start of the game. Yes, it's very functional in the right universe, but it's mostly a waste in the wrong one. If you do take aquatic, you might also want to make a point to set your galaxy to "organic rich" so there will be more planets that you'll benefit from during early expansion.
Now, if I understand that correctly, that means you start off with a Gaia home world,
and that you can also forego the "Gaia transformation" technology, as you won't be
gaining that much by it anyways. This seems like a rather large boost, so I must be missing something.
Well...yes and no. There are a bunch of factors, and it kind of depends.
1) The number one problem with aquatic is that is becomes obsolete. If you're playing a huge universe with 8 opponents, odds are extremely good that you'll research every technology that exists, and get quite a few levels into hyper-advanced technologies before you beat the game. In a game like that, all of your planets will be gaia planets anyway, and at that point, aquatic is doing absolutely nothing for you. Of course, if you're playing short games, that's probably not an issue.
2) As far as not needing to resaerch Gaia transformation...well, sure, but what do you gain by not researching it? At the stage of the game where it's practical to research it you probably have one to two thousand resaerch points every turn, so it's not so much a matter of "not" researching it as, "do I research it now or in a couple dozen turns?" Also keep in mind that the technology
after gaia transoformation is the evolutionary mutation, which gives you either 4 more picks worth of racial modifcations, or an extra 40% bonus to your score. You probably want that whether or not you're aquatic. Again, in a small, fast game where you're not planning on getting through the tech trees, this isn't an issue.
3) As mentioned above, to get the most possible benefit from aquatic during your early expansion, you should probably set your galaxy to oragnic rich. Which is fine if you want to do that. But it does mean not choosing normal or mineral rich. Which again, is fine. But it's an either/or situation.
4) Aquatic means that your home planet has more people, and the increased food production means you'll need fewer farmers, and thus wil be able to put more people on production and research. In all ways, this is a good thing, but the relative value of this diminishes as you colonize/capture more and more planets and the game progresses. Compare to, for example, subterranean, which gives a bonus to all planets regardless of size and class.
5) In a large universe, the real, true value of aquatic is that it gives you increased efficiency during a certain portion of the early-to-middle game. Sure...if you have a bunch of huge barren worlds full of starving colonists, yes it's nice to have your gaia homeworld be able to feed them all...but overall the gaia treatment of your home planet isn't nearly as important as the fact that once you start terraforming planets, suddenly all your terran class planets will be treated as gaia planets too. If you take advantage of that period of increased poroduction to capture a bunch of systems, aquatic has benefitted you.
math:
Don't quote me on these numbers, I don't have the game in front of me...but the way I think it works is that every planet is assigned a number corresponding to one of five size classes: 1, 3, 4, 5, 6. Tiny, small, medium, large, huge. The climate of a world multiples that number to determine the total possible population. Barren is x1, terran is x3 and gaia is x4. Homeworlds are medium unless you pick the "large homeworld" pick. So, by default, a homeworld would have a max population of 4x3 = 12. If you pick aquatic, your homeworld will be treated as gaia, so instead of 12 max population it would be 16. If you also chose large homeworld, instead of 15 max population it would be 20. Sounds like a huge difference, and it is...but compare to subterranean, which gives two times the size class bonus to
all planets regardless of climate. So, with subterranean your default homeworld would be 4x3 + 8 = 20, unless you chose large homeworld, in which case it would be 5x3 + 10 = 25. So, subterranean gives a much bigger max population than aquatic, and it applies always to all plantets. No need to wait to start terraforming to get the bonus to gaia class from aquatic. Even that small barren world you put your first colony base on will have increased max population.
Though, note that subterranean doesn't give you the increased food production effect that aquatic does. Even so, in my mind overall subterranean is a much better choice.
You could, of course, take both, which would give your homeworld a max population of 4x4 + 8 = 24, or 5x4 + 10 = 30 if you chose a large homeworld. Starting with a planet with 30 max population and increased food production on day one can be fantastically powerful in a small galaxy with only a handful of star systems. But ultimately, while aquatic is an adequete pick in a small galaxy, in a large or huge galaxy I don't usually find it to be of as much benefit as other choices I could make. In a long game, even a generic +1 research or production bonus would be of more benefit in the long run, and in a short game, cybernetic or unification would probably deliver more bang for the buck.
So it's not that aquatic is a bad choice. It's just that there are usually better choices available.