Hey guys, been a long time stalker but I've never been in a position to contribute meaningful dialogue or in a position to fly frequently.
This all changed with my new job! I will be flying to Seattle and Taipei, Taiwan at least once a month. My company always books the cheapest tickets (which I was told usually ended up being United and Eva Air). If the prices are fairly similar, they would allow me to fly whatever airline I want.
My question is which FF program should I join to get elite status the quickest? I did the 100k mile thing with BA last year and just finished the 75k x 2 thing with AA this month. Should I try to fly primarily AA to get to 1M miles?
Since Eva isn't part of any alliance... how would that work?
Any feedback or advice would be greatly appreciated!

Thanks a ton in advance.
Best,
PU2007