General advice from Brit expat 5 years in to SG:
British schools: Tanglin Trust, Dulwich College and Dover Court are the usual suspects. All good schools, all will have waiting lists, particularly in the early years (reception - year 2). North London Collegiate is opening up I think Aug 2020 so a good option as more likely to have places. Marlborough College is across the border in Johor, Malaysia.
Other popular schools: UWC, GESS, Nexus, Chatsworth, SJI, SAIS (Stamford International) or SAS (Singapore American school)
Lower fee schools: EtonHouse Middleton, Invictus.
There is a Singapore Expat schooling Facebook group which is really helpful.
Budgeting: rent will be around $5500-$8000. Obviously you can go much higher but that's about the average. Tenancies are usually for two years. Condos tend to have pools, tennis courts, playgrounds - makes it easy to make friends.
School fees - around $8000/term (3 terms per year) but again you can go much higher or a little lower 😉
Popular expat areas are Bukit Timah, River Valley, Holland Village, East Coast. Rents reflect that these areas are more popular.
It's a really great place to be.