Generally speaking, Phase 2A1 and 2A2 no need balloting... most schools start balloting earliest 2B.
For me, I had choice last year between St. Hilda's and St. Andrew's. SHPS is near, SAJS is far. But for me, my boy is quite active... think if he go to mixed school, he will surely be disciplined a lot, because compared to girls, he will be very disorderly, but if only boys, then he's just one of them... in fact, now, he is considered very good, because he is quite obedient and not as rowdy as some of the naughty boys. Also, at home, all girls except daddy, so want him to have more interaction with boys of his age. Also considered whether single session or partial only... I personally don't like afternoon session... waste of time... prefer morning. Then found out SAJS CCA on Friday morning, school end late on Friday for whole school... no need to worry about school bus. For both schools, he would be in 2A2, so equal chance.
(Er, why you say must move? If you in Phase 2a, no need to move cos no need to ballot... unless it's because you want to be closer to the school lah)
This year, I also have to choose between SHPS and st. margarets... I have two dd.. My DD's character such that I worry she go into BGR too early... so decide girls' school better. Anyway, SMPS make all P1 and P2 do gymnastics, which she like, and I prefer the dress uniform... plus feel that it's not so pressurising... so going ahead with SMPS even though it's further. Also, same, it's single session... better for us. otherwise so headache, one go, another one come...
Guess you know your children and your household routine best... you have to ask yourself what you really want out of an education lor... it's for 6 years, so think of the influence of the school on the child, and what the child will have to do during that time (fund raising, concerts, etc...) and how well the child will fit into the whole ethos of the school.
this is just my own experience... hope that helps.