Of course it depends on your child and what the best environment is for them and you may not actually know that until she starts school. i.e. How many in the class, is she distracted, would she need the help of smaller classes, or is she the sort of child that will do well anywhere?
We have just moved our dd in Year 2 to a private school and to be honest, it seems to really suit her and personally I feel it is one of the best decisions we have made, it is early days, but she is enjoying it and seems much happier generally.
There is so much to consider, not just the money, the travelling distance, where you live in relation to friends, the extra school work that usually goes with it.
I would suggest you visit all the possibles, including privates and then apply to the oversubscribed ones - if they are good ones, you can always make a decision at a later date.
Private schools however do tend to ask you to put down a deposit (£2/300), if you want to reserve a place, which you would lose if you then don't take it up.
Alternatively, try the state schools until Year 3 (juniors), this is the time that a lot of children start Prep school, but then your dd may have to sit an exam, which she wouldn't have to do to go in Reception.
Personally, I wish we had put her straight into Private, as there is some catching up to do now, however, those two years at State, gave us some idea as to what she needed and gave her the time to form friendships in our local community, which we will keep going, as her school now is quite a long way from where we live and the children who go there come from a wide area.
I thought our Outstanding State school would be as good an education as Private, but I couldn't have been more wrong!
Best of luck, choosing a school in the first instance and then deciding whether to move her, have been two of the biggest decisions we have had to make regarding our dd and the hardest, resulting in many sleepless nights! I don't envy you.