Put up a long moratorium to answer questions, fells asleep almost immediately after. Oops.
For reference, do contests still have categories like cool and toughness? That should pretty much counter the concern some people have about Joan's image problems.
My interest on the contest route depends a bit on how exactly they work for the context of the quest, but given that this isn't a hard vote, I might as well mark my interest for it. Otherwise I'd be perfectly happy to explore the world. While many of the involved trainers sound interesting, the current gym paradigm doesn't sound like something I'm all that wild about participating in. At least not until we got ourselves a baseline of training and are less squarely in the "get stomped, but maybe receive a pitty badge" territory. Then I'd be up to tip our toes into it.
Contests don't have categories the way they do in-game, but that's because they're all about impressing the judges and the public, and there's plenty of angles you can go at to do that, even if a lot of coordinators go for beauty and/or cuteness. But there's a reason they've managed for the most part to earn their status as a respectable career for Trainers. Individual contests will often have a theme they'll want you to work with, but will leave you pretty free to express it however you prefer. I guess the easiest way to put it is to think of them as all about finesse and control - whatever the impression you want to give is, the point is that it's about being able enough to make sure it's the only thing people see in your pokemon.
Also, there's no such a thing as a 'pity badge'. Sure, Leaders can give you a badge if you lose against them, but considering the whole point of leveling up their game was to keep out those Trainers not worthy enough of their recognition, it's less pity badge and more 'sure you lost, but I reckon on another day you could have won'. If that rankles, fair, but it's still a proof that one of the best Trainers on the continent is fine with calling you a peer and letting people think you are their equal.
And since I've seen a couple 'would [something] work as a Theme', I'll just put up a blanket statement : anything is fine, so long as you can convincingly explain to me why it's meaningful to Joan.
Also regarding Jasmine, considering like all the other Kanto/Johto Leaders I made up her team and Theme before the quest even began, you have no idea how funny I found it that you ended up with the same starter with a fairly similar build, too. Ever noticed how Melati seems quite knowledgeable about Mareep in particular ? From the moment I created her, I had Jasmine down as her best friend (it wasn't even subtle, what with the whole 'both live in Olivine, are close in age and Jasmine has a giant snake as her Ace'), so she's more familiar with the Ampharos line than most people, even if she's been happy to let you explore your own things so far. When the tutorial is over, she's planning to give you a standing offer to introduce the both of you if you want some advice.