I believe only AA credits miles flown on LY. So unless you want to go the long way from SYD-TLV with two stopovers all on OW airlines, then AA would be your only option for crediting.
Similarly, SYD-SFO would require a stopover in LAX flying on OW.
Have a look at the *A network too, that may be better for you.
My main consideration for choosing AA is actually buying miles on AA when they go on sale. They seem to have very good redemption value for both inside Australia flights and for SYD-TLV and they do not charge YQ on AA awards.
Do Qantas periodically sell miles at a discount like AA?