Things I knew about Nadia going in:

It had Hideaki Anno (Mr. Evangelion) attached
Fun character designs.

-- End of List --

Story

Based on the early episodes Nadia would have you believe it's about a mysterious girl and her mysterious gem, the group of villains who will stop at nothing to take it from her, and the young boy she befriends along the way (also there's a little girl and an animal sidekick mixed in there somewhere). That's a lie. False advertising. Bait and switch.

There is an adventure here, but Nadia is 39 epsiodes long, and honestly so few of those episodes pick up on the "mystery" of the the Blue Water story thread that only two conclusions are possible:

The show is packed with irrelevant filler
The show isn't actually about what it pretends to be about

There's so much time spent between larger story moments which don't really move the plot forward at all (even most of the more adventurous plot relevant episodes don't really move the plot forward actually) that the only way the show really works is when you accept and embrace the idea that the filler is actually the point.

So what is the show actually about?

For me, I think it's strengths lie as a character-driven coming-of-age story.

Characters

Nadia and romantic(?) male lead Jean are around 14 years old... and they are just the worst. Their character designs might mislead you into thinking they are older or more mature than they are, but in truth, any adult characters who acted the way they do would be intensely unlikable. The titular Nadia is unlikable. She is very much still a child who is figuring out her feelings (which often leads to her being flat out abusive, especially to Jean), and is the worst kind of vegetarian (the kind that will very vocally have a problem with other people eating meat around her).

Don't be too hard on her: she's a child.

Jean is a child too, in his own ways. He remains perhaps the source of some of the best episodes and character development in the series.

On top of that, the who ostensibly present as the villains of the series in the initial episodes (who have big "Team Rocket" vibes, or "Bonne Pirates" if you're cultured) quickly abandon their pursuit of the Blue Water, and instead join the side of the angels, becoming valuable role models for the children. They are replaced instead by a far more sinister group, who are conspicuously absent throughout the bulk of the series.

Random Thoughts

(Some spoilers here; none of it plot related)

This show feels like it was being written during production. The characters bounce around the globe in a series of disconnected arcs, almost never actually driving the plot. When the main cast find themselves in the action, it always feels like its either someone else's will, luck, or an accident.
There are a lot of unanswered questions that it feels like they just want you to froget about. I could list example here, but it would be too tempting to spoil something, and there's so precious little to spoil here I genuinely wouldn't want to, with one early exception: why Team rocket even wants the Blue Water in the first place (They claim they saw it... adverised on a poster?)
This series might be a prequeel to Evangelion? At one point there's a humanoid giant (named "Adam") that's supposed to be a proto-human. (Also a lot of barriers = AT Fields?) It's not really relevant (to either Nadia the show or Evangelion), but if not a direct prequel it's definitely a rough draft/prototype for the kinds of ~~themes~~ lore that would be recycled for Eva later on
There's a "10 years after" epilogue in the final episode. I won't spoil anything, except that one of the pairings is gross and fairly out of left field. If you were hoping for this, you're a creep.
The show has a certain style about it. The animation and character designs pop. The music is poppy and energetic (if not always ambitious or memrable)
They did a whole episode of character songs/AMVs once. That was kinda fun
Apparently it has a pretty laughably(?) bad english dub. I had never heard it until just a few minutes ago.
The whole series takes place in the late 1800's. That's probably worth mentioning.

In Conclusion

I don't actually like being negative, but I can't really recommend this. It's not awful when you understand what you're getting into, and indeed there's a lot here that I enjoyed. But not enough, and it's also a larger commitment than a typical 26 episode series. Even when you accept that the "filler" is the point, it's still pretty poorly paced. In fact, I'd probably rate it somewhere around St. Tail (a series I've reviewed prior to starting this blog; I'll probably post it retroactively at some point)

Even when it's applicable that you (or your kids) are in the relevant mood/mindset for a coming-of-age story, you have better options. (Castle in the Sky comes to mind, as does Escaflowne).

The only reason I can charitably support for watching this series is to experience the complete filmography of Hideaki Anno, and at least then I'm happy to say you'll get some Evangelion connections (or at least one) for your trouble.

Everyone else... have you considered watching Castle in the Sky, Escaflowne, or even Gunbuster instead?