I do saw milling, timber-framing, and furniture building in the northeast where both temperature and humidity swing wildly throughout the course of the year (even week to week sometimes). Here's a simple analogy I find useful to illustrate lumber drying and moisture content to folks: think of drying and storing your lumber just the same way you'd think of doing that with your laundry.
People get very hung up on things like "finished moisture content", kiln-dried vs. air-dried, etc. But really...it's all just laundry. Dry one tee shirt for an hour on the highest setting in the cloths dryer (kiln) and a second tee shirt on the cloths-line out in the yard (air dried). Yep, they'll dry at different speeds, and when you take the cloths-dryer one out it'll likely be "drier" (lower "finished moisture content") than the other one, but when you fold them both and put them in the same drawer, they'll reach an equal moisture content very soon. And that moisture content will be different on a humid day than it is on a dry day. And it'll be different tomorrow than it is today.
I talk to folks who are completely convinced that a good quality furniture piece or gun stock can't be made from air dried lumber because kiln dried material is both "drier" and "more stable". It will probably be "drier" on the day it leaves the kiln, but in exactly the same way that the cloths-dryer tee shirt is drier. And as far as "stability" goes, moisture stability is a myth, as Taylor and others have said above. But there's also a structural stability element which can be effected by the drying process and, IMHO, air drying is actually much better for lumber in regard to that. I've never shrunk a shirt by drying it on the cloths-line but my petite wife now wears several several things I've ruined in the dryer. And none of the beautiful early gun stocks we all admire are likely to have ever seen a kiln.
Anyway, the moisture percentage number that you're looking for is just not a number any of us can really give you. We can give you the one that's best for us, but not for you. The best answer for your time and place is to put your stock material where the temperature and humidity will most closely match wherever the finished gun will be stored/used, measure the moisture content periodically, and wait until the moisture reading stops changing appreciably (either up or down). That'll be the right number for you.
-John