2 important things to remember 1. that you must be an AA member for 30 days before you can purchase miles and 2. you can only purchase 150k miles per calendar year (the bonus miles you get don't count for this). Costs nothing to join so I would suggest doing this asap. I suspect there will be another generous bonus points offer before the end of the year which could help you warehouse points if you have a trip in mind for next year. Another bonus of the program is that you can book flights without having points in your account - you then just purchase the points you need and complete the redemption within 48 hours I think it is.
I have used AA several times for redemption on EY, CX, JL in J without problem. We are flying JL SYD TYO in J next month and recently looked at bringing the trip forward - J availability was a bit patchy but no problem getting F on just about any day. Cost for us using AA points for J one way was AUD$800 per person which included the currency conversion fee, AA's points purchases fees/taxes and JL's surcharges/taxes etc.
Some one world partner flights are available on line to book directly, with other partner airlines search for availability on the respective airlines FF program and then phone AA to make the booking. Not all airline reward seats are available to AA but I've not experienced this.