We all have different ways of picking which question to answer, so I can only speak for myself. The other guys are a lot more organised than I am!
My routine is to log in and read the new questions each day. See if there is a theme of the day, several questions on a similar subject, which happens surprisingly often.
Then I weed them down to the ones that interest me personally. I run a weekly tally of so many serious, a couple light and flippant and a couple harsh answers, so the questions have to fit the cycle too.
Next, look for questions submitted by regular members who comment on posts - if they are giving their time and wisdom to others, I feel obligated to do the same, though rarely twice for the same person in the same month.
And finally, the biggest selection criteria of all comes into play. Can I actually answer the question fairly and honestly? Usually yes, with research as necessary, but sometimes the answer is just no, I cannot.
This process usually gets me down to between 3 and 5 questions left open.
Then I coin toss for the one that gets answered.
(PS - yes, I know your question is over a day old. Sunday is traditionally a dry day for questions, so I go back further)
It's not eenie-meenie-minnie-mo?
I accept cash bribes. Or cookies.
I've got two criteria: how interesting is it to the audience? And can I offer good advice?