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With an income of $24K/year, you might not qualify for the Chase/BA Visa card. And that card has an annual fee which Chase typically does not waive for the first year.
More importantly, BA will charge you a hefty "fuel surcharge" when you redeem BA Avios for a SYD-LAX award. Better to use your AA miles, which will also entitle you to a free stopover in LAX, before continuing on to some other North American destination.
The FT MilesBuzz! forum is a good place to find current credit-card sign-up promotions.