Disclosure statement: I went to 12 years of Catholic school, my son just completed 13 years (including kindergarten) and my daughter is completing her 10th year (including kindergarten). My husband is a product of the Philadelphia public school system. It was a no brainer for him that I had a much better education than he did.
There will be frustrations with either choice, but I have found my interactions with Catholic school administrators much easier to handle than my (limited) School District interactions. Please note that my comments are comparing Catholic schools with Philadelphia public schools.
One thing that seems to stand out most prominently is that Catholic school parents, on average, care more about their children's education. The children are more disciplined and don't have to deal with a lot of the same baloney that goes on in public school classrooms.
As for academics, I can say that Catholic schools do not have a gifted program. If your child is tested as gifted, she will split her time with the Catholic school and the local public school for the gifted class.
Catholic schools teach to the middle; from what I hear, public schools teach to the lowest level in the class. Catholic school teachers will work with you and your child if you need more help or need to be challenged more. (My children were on the bright side, and most of their teachers pushed them to do better and expected more of them. Shall I mention here that both of my children received academic scholarships for high school?)
The grade school my children attended has a computer lab and a computer class where they were taught basic computer skills up to PowerPoint presentations, over to safe internet searching, etc. Not sure what is available in public schools -- could be more, the same, or less -- I just don't know.
You are allowed to ask your local public school and the Catholic school what they offer. I know the Catholic school would love to talk to you; I would hope the public school would do the same.
As for attending public high school, ask the Catholic school what most kids do when it comes time for high school. Where do they go? Not all go to Catholic high school although I imagine the majority does. Find out what the local public high school is and ask them about what they offer, how they handle discipline (and do they utilize a metal detector), what is expected of a student entering 9th grade. Some public schools have language requirements that may extend into high school. Not all do, but it would be good to know.
As for school districts providing related services, I believe that it is required, but it's not always convenient for Catholic school kids. Don't be afraid to call the school district to ask for what you need. You could ask about what is provided, where, etc. and get that information. Then you could ask how those services are provided for a child not attending a public school. May throw them for a loop and you may need to ask for clarification and confirmation since not all school district employees know how to handle non-public school student questions. Another story for another time, but trust me that it can be difficult, time consuming, frustrating, etc.
It's good to get advice from the people on this forum -- I've read many good responses to other questions. But ultimately you will need to ask your questions of the schools that are your choices.
Good luck to you.