Be aware that though the schools in Dubai are fee paying, they are not like a UK independent school, much more like a cosmopolitan, middle class state school. none are what you would call academically demanding. Though that does not mean the teaching is not of a good standard. Repton Dubai claimed to be like its UK mother ship, but it is not.
When you have a student body from over 70 countries, with a large turnover each term and especially in the summer, things are rather different. School sport is limited, though most sports are available in the city. When it is over 40 degrees in ths shade, you do not want kids outside for too long!
You are unlikely to find really small classes of say 15, as unless things have changed dramatically, there is always pressure on school places. Even if you start small at a newly established school, numbers will soon grow.
It is very commmon in Dubai for newcomers to take whatever place they are offered and then move to the school of their choice once a place becomes available. This is especially true at primary level. At secondary level there are a number of good schools, with the selective Dubai College having the most academic reputation.
Are you going for a "look see". Try and do so as it's really easy to get misconceptions about life in Dubai and seeing villas and some schools in the flesh will really help. There are companies that offer a school advisory and place finding service if you or DH's employer will pay for it. I don't have any recommendations, but I'm sure the British Dubai Women's Facebook page will help.