Hi @MightyMoe, sorry for the delay in replying, and please don't apologise - keep the questions coming, I'm happy to help!
As first gen to university it is really important to be conscious of what differentiates you from the main stream - there will definitely be something and it will only help you in terms of your applications to magic circle/ US firms.
In terms of working out which firms to apply to, I was very, very clear about the characteristics I was looking for in a firm and only applied to those firms which suited said characteristics. For example, I was personally only applying to firms with a) international reach b) office in Russia (I'm a Russian speaker) c) a clear gender equality strategy d) collaborative focus and culture, and e) pro bono which I was interested in. It was by tailoring my search profile for potential firms that I naturally tailored my actual applications. Given that the firms I chose had all/ some of those aforementioned characteristics it was very easy to transfer/ adapt my answers with a relatively short turnaround for each firm. Essentially, by tailoring the firm profile I simultaneously tailored my written application. I hope that makes sense.
I completely get where you are coming from in terms of magic circle firms seeming really similar to one another. I think ultimately it is up to you as an individual to differentiate between the firms by way of your experiences and preferences. To do this it is really important to try and meet the firm in some capacity whenever you can - Aspiring Solicitors is a fantastic scheme in that respect. Get a feel for the vibe of the firm, ask yourself - do you get on with these people? Can you imagine yourself working in this office? Are you excited at the prospect of applying? Why are you excited? Are there any differences in their training programme structures? etc etc. I know that is probably an unsatisfying answer but ultimately the firm wants to know why you prefer them over the rest, and I can't necessarily tell you that.
Wow you're a Russian speaker! Is there an opportunity to do work in Clifford Chance's Russian office?