(1) What is most important to you in a FFP?

Redemptions in business or first class. Would never do an economy redemption, I'd just buy a cash economy ticket. But if I can get a high status level on the back of my RTW flights for a couple of years that would also be good.

(2) How many miles do you usually fly each year & in what class? How many flights/sectors?

See my RTW at bottom of post. In normal years, I do 2 - 3 Europe-Asia or Europe-Australia trips a year.

(3) What types of fares do you usually buy?
PEY or Y.

(4) Can you choose your airlines and/or class of service? Do you travel for work and/or pleasure?
Yes to both. Work trips >5 hrs are in J.

(5) Which routes and airlines do you fly most often?
BA, CX

(6) What is your home airport?
LHR. HKG and SYD is also useful.

(7) Do you have FFP status of any kind in OW or other airline? What is it? Do you have any miles banked in a FFP?
BA Bronze; generate about 100,000 BA points/year.
QF no-status but around 300,000 points.
Star Alliance Gold.

(8) Preferred Airlines? Most common Airlines flown on?
Reply:
Economy: CX; also QF and BA preferred but flown long haul less often
Business: Anybody with a flat seat.

===

Well as noted above I have lowly status with BA and no status but 300,000 points with QF.

The 'Puff family comprising of Me, Mrs Puff, Mini Puff (4yrs), Micro Puff (1 year and travelling as a lap infant) are doing this RTW itinerary from January to July next year as a DONE6 One World Explorer RTW business class:

JNB-QF-SYD
SYD-JL-NRT
NRT-UL-CMB
CMB-CX-HKG
HKG-KA-RGN
RGN-KA-HKG
HKG-AA-LAX (operated by CX)
LAX-AA-ORD
ORD-AA-CUN
CUN-AA-JFK
JFK-AA-BDA
BDA-AA-MIA
MIA-AA-SCL
SCL-LA-GIG
GIG-BA-LHR
LHR-BA-EBB

We will also be doing in economy:
SYD-MEL-SYD
SCL-IPE-SCL

I need to pick a FF program for these flights. Note the lack of BA metal which makes me reluctant to use BA with the minimum 4 (?) flight segments to get increased BA status. There are 3 x QF segments. But I can just take another QF flight somewhere to make up 4 x segments which is required to get status on QF.

My QF anniversary is between the first JNB-SYD flight and the second SYD-NRT flight. Mrs Puff and Mini Puff are also QFFF members but I can't find their login details to work out when their anniversary is? I may be able to join them up with a new account as they have both changed passport numbers since changing the first time?

So question is: what is the best FF program for me? Is it QF or is there some other option I should consider such as AA? I've seen AA platinum challenge mentioned but have no idea what that is.