There are a number of good questions that were proposed at the start of this thread, but rather than address them all individually, I'd like to just address the first ones about the individual Pokemon, referencing the kind of things the other questions ask about throughout.
(Water). What types can make effective use of defensively-oriented moves that coordinate with eligible abilities?
I want to start off by addressing this question because I think it is actually the type we can be the most free with. The simple fact is, "defensively-oriented moves" are not going to care about typing. These are status moves and offensive moves with side effects that are not caring as much about STAB. So to be quite honest, I really don't think we should be worrying about move/ability synergy when dealing with this typing. Rather, the most important thing here will be picking a type that can support a solid defensive Pokemon, but that does not put it in direct competition with anything that will likely outclass it due to the limitations we will have on its stats. With that in mind, I think we should probably avoid Fighting, cause of the direct competition with Arghonaut. I'd also be a bit wary of picking Ground or Poison, as Gastrodon and Toxapex, while not far beyond what we can do with stats, are so solid in their niches that I feel it would make it difficultto not end up quite similar to them, and possibly just replacing them if we want to be good. And that would not be quite so interesting.
Instead, I think where we should be looking for our Water type is to combinations like Water/Steel, Water/Dragon, Water/Fairy, or even just pure Water. Types like this are very solid defensively, overall, and either lack good Pokemon of that type combination, or have the best Pokemon of the combination lacking a key trait (most notably recovery) that we could easily utilize to let us not be outclassed, despite what will likely be lower stats.
(Fire). What types have healthy STAB movepools that they can coordinate with eligible abilities for offensive use? What types might be better suited to coordinate with an eligible ability as non-STAB coverage, due to their faults defensively or otherwise, and why?
Next I want to talk about fire types. Crucially here, we want to be offensive, which, very much unlike our Water type, means we really need to have types that can take advantage of potential abilities with its STAB offensive moves, for the sake of the concept. As such, even if a type is good offensively, if it lacks the moves to give us a number of viable ability options, then we should probably avoid it. And, as has been brought up be a few people already, this really means that we should avoid Fire/Fairy, despite it being a fantastic offensive typing, as fairy has so few moves for us to take advantage of, and therefore so few options for us to pick from in later stages.
So, with that in mind, there are a few specific types that I have been thinking a lot about. Fire/Rock and Fire/Flying are two types I like because they both posses a lot of different options for the abilities that we are going to be choosing from. Low accuracy, secondary effects, recoil, you name it. Rock in particular has a ton of different options in this regard, but I feel is a slightly worse type generically for our Pokemon when compared to Flying.
Another pair that I really like a lot are Fire/Electric and, my personal favorite, Fire/Ice. These two are types that I feel may not have quite as many different ability options as the previous two, but mesh even better with our Fire type for what we are trying to achieve. Both Electric and Ice are similar to Fire in that they have pervasive secondary effects on their attacks, which opens up a number of options. Unlike Rock, which leans heavily physical, or Flying, where our ability choice will have huge effect on whether we want to be physical or special, Ice and Electric are much more open. Nearly every single competitive move of both types has some effect that can easily tie into an ability, and many are available in both physical and special. Furthermore, while both are great offensive types, the combination with Fire leaves some substantial gaps on both, especially Ice. I actually think this is a good thing, as it also opens up the option for us to greater utilize our ability with coverage moves, not just STABs. It also gives us much greater control over what kind of checks and counters we do and do not want to have. Some of the abilities we may be looking at are very potent, and so will make coverage trickier to deal with. So the ability to simultaneously have a powerful offensive type while also having a number of natural type based checks will give us a lot more flexibility in what we can do.
Finally, I also do just want to say that, much as I know people don't want to hear it, Fire/Fighting would also be a pretty darn good typing for this Pokemon. Lots of move options, just like the above, while being one of the most solid overall types. While we have seen such a Pokemon before, they are hardly relevant nowadays. Blaziken is too powerful, while Infernape and Emboar are too weak. But with that, said, I think these Pokemon can serve as nice examples of how the typing can fail in the current metagame, while allowing us to be safe in the knowledge that if a starter Pokemon of that type can be both too strong and too weak, it should be easy enough to make one that is just right.
(Grass). What are some underexplored types that have the potential to allow us to create an as-of-yet unseen niche for CAP 25g? How does this typing help us to explore our concept?
To be honest, this is the type I am the least sure about. With less of a clear offensive or defensive focus, I would put less emphasis on directly utilizing STAB moves with abilities than I would for the Fire mon, but certainly I would keep it in mind, unlike the Water mon. Avoiding the types most commonly utilized by good Pokemon is, like with the Water mon, probably ideal, as we may have a hard time competing with our limited stats. But of course, reachzero is right in saying that just because good Pokemon of a typing exist that it doesn't mean we have explored all ways of utilizing it. I'd probably want to stay away from Poison type, as just about every way of trying to use that type combo exists, but beyond that, I don't have a lot of solid guidance on where we should be going. Of the types suggested so far in the thread, perhaps my favorites are Grass/Electric, Grass/Flying and Grass/Ice, but I do not have as solid an opinion on any type combination here as I do for the others, and I will likely post again with any further thoughts if I decide on a preferred typing.