Phoenix International School

Phoenix is a very small school and mainly caters to British students so although it will be easier for your child to settle and make friends they will miss out on spanish life and making spanish friends. It's also quite far from where you plan to live so you have to consider his social life too with his school friends, there will be a lot of taxi mum!. 

 If you're planning to stay here long term then a bigger and more expensive international school is your best option If you have to go down the private school route.

 El limonar, kings college or new castelar are the 3 main ones in this area. Also phoenix and el limonar are the furthest from the areas you've said so it would be a good 25/ 30 mins each way, although most of the schools have school buses at an additional cost.  Kings is the most expensive followed by El limonar, They both offer british qualifications. New Castelar is the cheapest. All decent schools. 

An alternative would be a concertado, these are semi private, you pay a small fee but they are mainly government funded. The best one in the area is Las Clara's but they usually have a waiting list depending on the year group.