1. What subject?
The first and potentially easiest way of choosing your university is deciding what you might like to study. Here’s an easy exercise - if you’re applying with A levels or some equivalent through UCAS, open up a spreadsheet in Excel, write down the names of some universities (choose them at random if needs be!) and see if each place on the list even offers the course you want. Mark down the grades you need at each school and then rinse and repeat for as many subjects as you want - this is a nicely organised way of working through it and will make it easier to compare your options.
You’ll normally find all the relevant information on the university website, such as the aforementioned grade requirements, details of the application process (entrance exams, interviews etc.) along with aspects of the course that might be specific to that school - this is a great means of learning more about what each institution offers and might entice you towards or even repel you away from a particular place. This sounds negative at first, but in both cases it makes the final considerations simpler.
2. The Russell Group
Listen, I am not (or at least would not like to think I was) an elitist when it comes to education - I was happily state-schooled, and I have met people from an enormous range of backgrounds in the academic sphere who were all fantastically competent. By and large, I do not think that whether a university is part of the Russell group should sway your decision.
However, in my opinion, if you are considering biology or chemistry I would perhaps let it play on your mind just a tad. My reasoning is this: In such a university, your lecturers are more likely to have their own academic research going on which will enhance your chances of extracurricular opportunities in this area (see point 4). I think there are sufficiently few people taking maths and physics courses at present that demand exceeds supply for competent graduates in these areas, but this does not appear to be true as a whole across the sciences.
This is very much a generalisation, and many people will disagree, but this goes for all subjects of study - if you think that academia as the endpoint could be what you desire, (or industry research for STEM fields), then I think I would be doing you a disservice by not at least suggesting that you look into this aspect.