@Hoardasurass has given good advice. However, I'd like to add a note of caution: in a mainstream secondary setting, "support" often only consists of a restricted timetable, access to a support base when overwhelmed and sharing a Pupil Support Assistant with other children in class. (That was my experience as a PTC in another part of Central Scotland.)
Therefore, if special school access is at all possible, then that would probably be better.
I've worked in two campuses which housed both a mainstream school and a special school. [The latter term is still used in some Scottish authorities.] In that situation, it was sometimes possible for pupils from the special school to take certain subjects within the mainstream school, but with one-to-one support provided by the special school. [N.B. I retired from my permanent post 7 yrs ago, but only came off the teaching register last year.]
I don't know whether a similar set-up is available in Edinburgh, but it would be worthwhile making enquiries. I've found a link to a directory of special schools in Edinburgh. Clicking on the bold letters gives you the links for schools: those in turn have links to their full websites.
I don't wish to dishearten you, but the LA that I worked in stopped providing support for pupils within mainstream once they hit their 16th birthday. They'd still get exam accommodations, but no support within class. As a PTC I argued about this, but was met with shrugs.
Schools would encourage parents to consider college courses for S5 and 6, with the argument being that the children would be welcomed there since the colleges got extra funding for those with special needs.
If it looks like a mainstream school is the likely outcome, pay special attention to their support mechanisms. In my experience, in some schools, SLTs have tried to save money by combining specialisms.
For example, in one school we had Guidance Teachers, Behaviour Support Teachers and Learning Support Teachers - ideal. The school needed to save money, so they were combined into one Pastoral Department led by a former Guidance Teacher, so that there was no longer a need to pay three heads of department. The Guidance Teacher was lovely, but had no expertise in Learning Support.
Also consider the size of the school. Children with additional support needs often feel overwhelmed in the largest secondary schools.