Mostly just Discovery and Picard is kind of halfway there.
SNW is a really fun watch once they've dealt with Pike's future (which they kind of really have to). Personally I like that they go for different genres, but I can see why some people might not like that if.
Lower Decks is a riot and a half and I think it's my favourite Star Trek, but it might be kind of cheating because it stands on the shoulders of all the other shows.
Prodigy is quite a bit different from the other shows, but it's full of optimism, hope, and friendship. It doesn't start out that way, they're all very suspicious of each other at first. They grow into it as they learn more about themselves and each other, and aspire to be part of the Federation and Starfleet.
As a fountain pen user, I would suggest against that unless you know it suits her personality. Fountains pens require maintenance, and certainly it's easy maintenance, but it's definitely more work than a ballpoint. They are a hobby, and if it's is not her thing, she'll never use it.
I would instead recommend a nice ballpoint pen set where the ink can be replaced when empty. Something she can use without having to think about or maintaining it.