DTQ..
I'll echo what Dave posted in his reply for all the reasons he mentioned...esp. the part about keeping all 4 elements of the play in front of you...ball, base, runner, fielder. You've got the prorities covered and you're now where you need to be for the "money play" at the plate.
Two things your OP did not mention that would bring some other factors into consideration, but would still be covered by the suggested positioning that Dave recommended.
1) How many outs?
2) Position of BU at start of play. B? C? (Your OP did not mention if you were working SP or FP).
The reason for my asking you this is if in your sitch. there was 1 out when the ball was hit you have a possible Time Play. Catch by F7 is 2nd out.
R1 tags...F7 throws to 2nd (rather than HP) R1 is tagged out for 3rd out...did R3 score in time?? Following Dave's recommendation you now also have the play at 2nd (and the timing of BU's out call) if not directly in front of you, it's certainly in your periferal vision.
My reason for asking abut BU's position is that he has to position himself to see the catch and his R1 tag up responsibility...as such your getting some catch/no catch help right there without BU going out.

Very good point that I quite clearly missed. If the throw had gotten cut off and sent to 2B, the only way you'd be able to tell if R1 scored is if you somehow got past the 1B foul line, which means an extra 10 feet of hustle (remember those 4-5 feet from earlier?). Calling the catch from fair ground puts you at an even bigger disadvantage when deciding whether or not the run scored on a timing play.

Good catch, KJUmp.