My dad is going on the following trip this summer, and is currently not a member of any frequent flyer program. He's asked me for advice about what program(s) he should join...

All Economy Flights:
MAN - SIN Singapore Airlines
SIN - PER Singapore Airlines
PER - CBR Qantas
CBR - SYD Qantas (QantasLink)
SYD - WLG Qantas (JetConnect)
WLG - SYD Qantas (JetConnect)
SYD - SIN Singapore Airlines
SIN - MAN Singapore Airlines

He generally doesn't do long-haul flights, but does fly in the UK domestically and in Europe on a semi-frequent basis, so I was thinking he should probably join programs for UK airlines rather than SingaporeAirlines/Qantas ?

I was thinking maybe he should join BMI's program for the Singapore Airlines points, as he's more likely to rack up points with BMI after this trip.
Then I thought maybe he should join BA Exec club for the Qantas flights..?

Any advice about a better strategy would be greatly appreciated.
Thanks...

Yes, BD definitely makes sense for the SQ segments. Do double-check that the booking class is eligible for BD miles, though (see here for table of eligible booking classes). As to the QF segments, the problem with BA is that you will only get 25% mileage on discount economy. It is worth looking around at other OW programmes, AA in particular, to find out whether it would make sense for him. In any event, flights on BA itself in discount economy will earn miser miles, whichever FFP you credit it to.

If your dad only need "award miles", then he can enroll SAS EuroBonus.

Earning rate on SQ flights
Earning rate on QF flights

But as NickB says, please double check booking class on SQ/QF flights.

thanks for your suggestions.
It's much appreciated.