1) When you are ready for her to start classes.
Generally HK kids start classes around four, following the British system that was put in place. But the 4-year-old start date in the UK is getting a second look as some consider rushing education at an early age actually does more harm than good. The US is currently age 5, the UK is looking at moving it back to 6, and some countries like Finland don't start until 7.
At age 3, you might look at doing some things social with her, such as an organized playgroup or meetups. Not so much to drill them in flash cards but to get them more comfortable being around other children. But when to start something formal is something best discussed with the potential pre-schools you are meeting and your own read of your kids abilities and desires (and also yours--you may want to just spend more 'kid' time with them). I'm a strong proponent of "let children be children" so take what I saw with that bias in mind.
2) I'm gathering when you say "she will have to attend an international school" what you are really saying is "she'll need to attend an English-language school". ESF is the 'semi-public' school system for English-speaking parents, and there are also Direct Subsidy Schools that teach primarily in English I think. They aren't quite the same as the private international schools that charge considerably more per year and that you read about.
As for a pre-school or kindergarten being a 'feeder' for a specific International school, I think there's more smoke than fire there. Kids come in from a variety of pre-schools and kindergarten programs such that I don't think anyone is going to push you to one school or another.
3) Define 'best'?
Kids learn differently. What is best for your kid is not necessarily best for some other kid, especially at these earlier years. What might be best for the kids who will "memorize and learn how to take tests" may not be best for your daughter and the future educational path she may take.
I think you'll find there are some schools that are more sought after than others, but ranking 1-2-3 isn't really helpful as it is apples and oranges.
Sought after schools would include, in no particular order, the Kellett School (British), French International, German-Swiss International, HK International School, Canadian International, Hong Kong Academy, ISF, Chinese International, and my apologies to the few others I didn't list that all have long wait lists.
