[Please excuse me stumbling in with my blunt and half-informed impressions....

]
But first up, welcome to the forum!

With such a housing budget pretty much the whole of the island is your potential oyster. We produced a tool/FAQ to assist this necessary triangulation here ->
http://forum.singaporeexpats.com/viewtopic.php?t=101985
Most intnl. schools, and many local ones run shuttle buses across the island. So immediate proximity might be less of an issue than a new arrival imagines. To me, Woodlands is not a particularly nice place to live.... new town, soul-less, very local, a heck of a long way from home comforts if and when you want them. But of course close to SAS. So I'm sure there are
condos there with plenty of families with children that attend that school. If the bread-winner works locally perhaps this works well (no idea), but I wouldn't wish it simply to give convenience for the children at the extent of the rest of the family living in a relatively distant back-water.
Sentosa. Again not somewhere I know hugely well, I've been 3-4-5 times. [Consider why so few times, not least that it's a bugger and $ to get to]. It's not that long ago it was effectively a prison island for political prisoners. What now, fla$$hy-trashy yacht clubs and theme parks, plus enclaves for regional tax-exiles. Woodlands is 'real', and perhaps too real for many expats. Sentosa is completely fake and at times verging on surreal. In some ways it's easier getting to BKK or KUL for a w/e, than being invited to Sentosa for an event.
So if you consider that that is probably why D10/Holland works more for many people in these circumstances. You have the school shuttle-buses. The proximity to downtown (work), 'people like us' down at the pool, groceries with western goods down at Orchard, etc. So that might be the default/core to consider, but you have to push out the boundary just a little beyond the D10 mecca and your budget will get exponentially more.
Many schools have after-hour activities, since many parents put in long hours. The school's website should elaborate.
I forget if the major grocers do home delivery. We'd sometimes see Cold Storage vans come to the
condo, but I think the assumption is that coined-up expats will have domestic staff to do the shopping for them (and hence a question to consider for you). Otherwise on-line shopping seems (IME) very undeveloped in SG, I expect the critical mass of market size just isn't there.