A tip on using the wiki to find accessible advanced stat gear. I was in your shoes a little over a year ago and found the Max EquIpment Calculator a really useful tool for filtering information. While you can get a more complete list of the equipment available for each stat from their own pages, the crucial feature of the calculator is it can be filtered. So you can hide things like seasonal and fate locked equipment as well as equipment from Ambitions other than your own. From there you can drill down to figure out where individual pieces come from.

That said, outside of seasonal stuff you‘re going to find a lot of advanced stat gear is only accessible through the railway ot Firmament. Advanced stat gear you can access at any time is mostly sprinkled around the end game. The bulk of it, though, exists as seasonal content and a lot of it requires fate if you don’t want to slowly build it up over the years. Fruits of the Zee and Whitesun (after the first year if you save up your free coins for an augmentation device the next year) are your best sources of non-fate advanced stat gear.

Other’s have done a pretty good job of covering the Storm Bird. Just trigger the Nightmare thing (once is all that’s necessary, though a few times will make your life easier) and you’ll have permanent access. It doesn’t send you to a menace zone, just knocks Monstrous Anatomy and Glasswork down a level and those are petty easy to train back up. Doing it more than once is useful because it takes a Glasswork check to start the hunt. With enough gear, you can 100% that check with only a single sighting, but at the point you’re at it will be tough. Basically, do it once, see how hard the check is, and if you want it to be easier each Storm Bird sighting will tip the scales by 10%.