Credit cards which earn frequent flyer points is a popular way to earn frequent flyer points. You can receive thousands of points on everyday spend. And, many of these cards offer generous signup bonuses! Compare to find the credit card that best suits your needs.
There are a number of ways you can do the trip. Which is the best way? That is up to you. Do you want to go to ATH only?
A return award PER-ATH is 128,000 points + taxes and charges. One possible route is PER(QF71)-SIN(QF31)-LHR(BA640)-ATH(BA631)-LHR(QF32)-SIN(QF72)-PER. As I mentioned before you can route via HKG or even NRT.
If you want to visit other places, and have the time to do it, then why not redeem a OneWorld RTW award for 140,000 points (142,500 points if requiring phone assistance) + taxes & charges, including up to 5 stopovers and a limit of 35,000 flown miles. An example itinerary could be PER-SIN-LHR-ATH-MAD-JFK-LAX-HNL-SYD-PER.
QF FF awards are not available using codeshare flight numbers with the specific exception of LA operate flights on SYD-AKL-SCL and return. All other QF FF awards must be on the operating airline's flight number. And since GF is not a QF FF partner, you cannot use QF FF points to redeem awards on GF operated services.
So you will need to route via LHR using BA for LHR-BAH-LHR and the again use BA for LHR-ATH-LHR. It will probably be most cost-effective to use the OneWorld award and include a CX or IB flight in the mix to ensure you have two carriers other than QF. That award is based on the total miles flown (as opposed to one-way trips for other QF awards) and includes up to 5 stopovers.