What do you mean by backbone? You mean backend implementation?
I see three identical attachments. Was that intentional or a mistake?
Also I find it comical that your school is asking to implement the store section of your "thesis" project (my assumption) using Linked List. If this is Java a backend, I can't help myself but laugh at the school who's asking you to do this implementation.
I'm not a Ruby expert but I've played with it. If you have limited time, I suggest doing this in Ruby on Rails You must register or login to view this. but if you insist in Php use a framework like Laravel.
I'd give you some tips though how to disect this project. You should approach this with a three tier approach:
Backend (your PHP app). This acts as the gateway, the backend for frontend, the backend service for your frontend
Persistence layer (MySQL, PostGres etc
Personally I'd approach this with a microservice approach but I get the impression that it might be too much for your team right now.