Basically:
I have 20 Fate burning in my pocket, and am not sure upon what to spend it.
Storylets I already have:
• The Labyrinth of Tigers Extra-Special Breeding
• Every story you can buy from the Fate page— Rubbery Murders, Soul Trade, Long-Lost Daughter.
• Flute Street
• Secrets Framed in Gold
Storylets I have yet to explore:
• The two fate-locked Etiquette items in Mahogany Hall
• Deeper Into the Foreign Office
• The Velocipede Squad
Qualities I’m curious about:
• A Warrior’s Code
• A Power in Waiting
• Fist of the Bazaar
• Hellfarer
• Empire’s Kingmaker
A. Does anyone have any advice on what items I should take?
B. Any tips on what leads into those mystery qualities? My interest has been piqued!
Without wanting to give too much away (this is fate-locked content after all), it sounds like you haven’t fully explored all the stories you’ve already bought, given the qualities you’re curious about.
Of the stories you’re considering, I have only done the two pygmalions in Mahogany Hall. I enjoyed them. I get why some people think they’re less good than other fate options, but I found them good fun.
And just in case you haven’t bought exceptional friendship yet, that is the best use of your 20 fate, certainly first time around. There are at least two excellent stories waiting for you in the House of Chimes.
I have already had a subscription in the past. The stories from within the House of Chimes I’ve done.
Regarding ‘haven’t fully explored’, I have finished all of the Fate-Locked stories I have bought. I have not, however, gained these qualities. Perhaps I took a different path?
I’ll try the etiquette tutoring. They promise to be good!
The A Power in Waiting or Empire’s Kingmaker quality (I don’t recall which one, exactly, but it’s one of those) is connected to [color=rgb(255, 255, 255)]the deeper matters of the Velocipede Squad[/color]. Exactly how will become obvious at its very end.
Regarding the story lines you may not have fully explored yet, has [color=rgb(255, 255, 255)]the Bishop already commented on your brand new horse[/color]? If that has yet to happen, there’s quite a bit of (Opportunity card - based) content yet to explore. Note that the qualities you acquire at the end of this storyline may be mutually exclusive.
As for the remaining stories, I’d recommend The Velocipede Squad. The Foreign Office storyline is interesting, but it just sort of fizzles out, and the Etiquette items are quite amusing, but not so much fully-fledged storylines as small distractions.
Oh. 
That’s the one fate-base story I’m still in the midst of exploring!
Thanks for the advice. :) Onward I go~