The other thing I would say (from experience) is it's no good saying 'ideally I'd like a school near home.'
It really doesn't work like that. You go where you can get all three children into the least worst place in the end, and it may end up being on the opposite side of the city.
If at all possible, get your school places first, then choose your long term house or you are in for a potentially horrendous school run. Look at proximity to DH's place of work as well, and pick your neighbourhood in a place that works for both.
Even saying that, it can be a nightmare because schools will break up in the next week or ten days and you'll get radio silence until September now. You won't be able to visit, they won't be able to interview your child etc, so realistically you may end up moving out there first and confirming school places much later. Be prepared for them not to be settled in school until October half term.
If you end up having to commit to renting a house before school places are offered, I'd say be prepared to move after the first year, once you a confident that the school is working out. Don't worry too much about finding exactly the right house at the moment, you won't be committed for more than a year and that is easier to change than the school or the school run!
Try not to sign a lease on anything in August or September - stay in a short term serviced apartment for as long as possible. If you want to move house it makes it really hard to look for new one when the changeover period is disrupted by the summer break (you will probably go back to the UK.) It's a pain if you need to move out of your current house in September you are not around to look for another one in July and August!
Be aware that some of the compounds come with a monthly fixed fee on top of rent for utilities rather than you paying direct to the utility companies for whatever you use, and these can be EXORBITANT. Ask the right questions, ask to see evidence, don't take anything at face value and don't trust anything you are told verbally.