depends on what booking klass you are in on both airlines. You won't get much if you're in deep discount singapore economy on any airline program however those UA flights could pickup a few miles. Not enough for a flight you'll be able to redeem for free in AU anyway.
Personally I think you're better off not joining any FF program and going to see a shrink because you've obviously made a poor descion by not choosing QANTAS and ONEWORLD on both occasions.
I would suggest joining the UA Mileage Plus programme
You will earn 7,400+ miles each way for the trip , which is a reasonable way towards the 25k needed for premier status
If the flight on Singapore Airlines is in a mileage earning class then you'll earn the mileage from that flight to your account too. I would contact UA and verify what booking classes are eligable for mileage earning on SQ. Assuming you book an eligable fare, you will get full miles and should attain Premier Status with UA
np. Check the booking classes and make sure that they are eligable for mileage earning by giving UA a call. not sure where they put the eligable fare bases for SQ on the UA website. If eligable, then you'll soon have *A Silver status
Picking on price rather than FF miles is a v good way of choosing flights ( within reason... still wouldn't convince me to fly MS again for example )