Cartridge pens are slightly less cool than bladder/lever pens but much cleaner and more convenient.

I've got a couple of each, but nothing particularly fancy. The big pen names like Parker, Pilot, Mont Blanc (if you're feeling flush) are more or less comparable and usually have more than one price point.

Not really, the cartridge is just a reservoir with a partially perforated spot for the ink tube to poke through.
Some brands are bigger though, so check what size the pen wants, then go nuts.

One cool thing is to get a restored Esterbrook pen for her. They were common in their day and often used by secretaries with less-than-large cash reserves. At the time they were maybe a $3 pen. They look and function very well (I have 3 different ones), can be nibbed based on the type of use you're planning, and are not as expensive as some other options out there.

There's also a new "panache" about carrying a restored, 60-year-old-pen.

I see that Esterbrook has been revived as a brand. But I still have my Grandfather's original Esterbrook pen with the ink bladder.

The bladder actually lasts a good while for each fill, but I discovered it was very impractical for heavy writing in mobile situations (eg high school or college notetaking) due to the refilling method. A cartridge is a lot easier to carry a spare and pop a new one in if it runs out during class.

But super cool!

The school I went to required us to use fountain pens through graduation.   

I can’t understand why anyone would use one by choice.  But that’s just me.

The inconvenience hardly outweighs the subtle flair it adds to handwritten script.

The nib is what is really important

https://www.jetpens.com/blog/guide-to-fountain-pen-nibs-choosing-a-fountain-pen-nib/pt/760

Not recommending this site, just what I found on a quick search explaining it.

We can discuss different ink types next, along with paper selection.  Don't forget to wear your pocket protector.  D@mn things leak.

A fountain pen killed my father