There are 5 primary schools in our area. We applied to three (two were just awful, heard very bad things from reliable sources), but we only wanted the one we got, thankfully.
The most popular and over-subscribed bunfight school consisted of several portacabins that looked like containers from a ship, with a bit of pladtic across the middle 'corridor' to protect children from the elements when they went from class-to library-to lunch. Oh, and a delightful but fenced off area full of trees and wendy houses and tyres-on-ropes... that Reception kids were allowed to play on on Thursdays. Other days they were to be on the gravel surrounding the portacabins with mo shade. In 35° sun (abroad). All the poshos sent their kids there, for some reason.
We got DD into the school-shaped-school where you can hear the loud hum of happy children, with a lovely garden, delightful staff. A mare to park in the morning, but hey ho.
Both schools are state.
I think most people try to get their child into the right school. But the right school means different things to different parents and different children.
All the private (semi-private, actually) schools here are religious. Peolle send their kids there whether they're religious or not (and these days the nuns aren't picky, they'd sell their own mother superior for money), but there are no immigrant children so they're popular as hell. We could afford to send DD there, but I don't like that attitude to life and would rather DD doesn't grow up to be an arsehole.