"Basic economy" is a paid booking category (with even way more restrictions than regular economy). The lowest award category is "economy". So are you trying to find an award flight, or book a paid flight with points?

Yes, the awards available to partners may not be the same as available through AA directly. You can do a search for AA partner availability at www.awardnexus.com (sign up for free as a FlyerTalk member by clicking "more signup options" under the green Purchase button) using either QF and/or BA with the same user interface.

You have to choose among these:

OneWorld

• Cathay Pacific Asia Miles (CX)
• Malaysia Airlines Enrich (MH)
• Qantas Frequent Flyer (QF)
• Qatar Airways Privilege Club (QR)

The only one I have any experience with is Asia Miles, and I gave that up when they demanded my mobile phone number for two-factor authentication (no other form of two-factor authentication possible) just to maintain an account with them!

You'd have to look both their award charts and routing rules to figure out which would be the best value. Routing rules can clobber value if you're not aware of them. For example, AA itself doesn't allow you to use QR (Qatar) for routings to anywhere other than MIddle East,, Africa, and the Indian Subcontinent as a single award. Anywhere else you fly on QR connections, you have to use two separate awards (which is almost always more miles than one award). I know that' not where you're flying, but that's just an example of how you have to be aware of routing rules, not just award charts. Every airline can have different award routing rules for awards between A and B.