If the ball is clearly past the Center Fielder, run hard and pick up the 3rd base coach while doing so.
If the ball is looking like it will probably be caught by the CF, go as far out as the base runner can go while still being able to get back to first base in time to beat a throw after the CF catches the ball. Lots of coaches instruct "go halfway", but it's really more about how far you can get out while still being able to get back to first in the event of a catch.
If the ball is looking like it might drop in front of the center fielder, the base runner should go as far as she can while still being able to get back to first if the ball is caught. Once that ball is down, sprint like crazy to 2nd base.
If the ball is looking like it will drop in front of the center fielder, the base runner has to go all out for 2nd.
If the base runner misjudges the fly ball, it's just more data into the memory bank. But sitting on 1st in this situation doesn't make much sense, assuming the ball has cleared enough real estate that the base runner can still get off the base without being thrown out upon a catch.
BTW, we believe that for the data to find a solid home in a memory bank, this process needs to take place without the base coach calling out everything. When the base runner takes responsibility for judging how the play is likely to develop, that's when she gets data that will help her in the future (whether or not she is correct when she judges that particular play). The base coach might yell "that's down" or "she's burnt" to help the base runner, but the base runners on our team know they still have primary responsibility for judging the ball and making the base running decision when, as in this scenario, the ball and the play is in front of them.