hi Alto, I gather from your parallel thread on SPSG that considering going independent is a new option?
Your Head had put your DD on the summer camp, so when you return to school, taking to he/she may be a good starting point. Your DD is obviously smart, but her personality may be suited to some of the selectives more than others. Re costs, if you consider St Paul's as the most expensive (circa £22k per annum before year on year inflation) then the others will be less. Talk to each school's bursary dept separately as each school's thresholds differ. Scholarships can also help, subject to being awarded one/more.
Look at where you live, what you want the maximum commute time to be (and how. use TfL planners etc as this could rule out schools from the start.
Do you want girls only or open to co-ed? What things is she interested in?
To get the ball rolling and a feel for your nominated schools, get onto to the open days (the dates should be open now and fill up quickly). Be mindful that these are opportunities for the schools to sell themselves, but a start.
Finally, (apologies, all this is quick and dirty advice), once you've trawled the league tables, websites re indie schools etc, keep on forums such as these/11+ forums etc and review past parents feedback. Invaluable insight to stuff the school gate guys won't tell you!
If cost is a real issue, be mindful not to start the process unless you can genuinely afford independent secondary as an option, as bursaries are tough to obtain as reality is there are only a handful available (at variable levels of % support) for families in need. So work out your bottom line if your DD was to undertake the process. Or sacrifices are made for 7 years that can impact the wider family etc.