What @CanOfMangoTango said. The classics she listed have stood the test of time. The Pegasus are on model what, 44, now?
But all those listed are quality cushioned running shoes that will suit the vast majority of people. And you won't know if they suit you until you've got a fair few miles out of them.
Gait analysis is a very handy way of getting people to part with their money but nothing more than that. If you are having foot problems then go to a podiatrist and have someone qualified look at the issues. Not a salesperson.
In gait analysis, all that will happen is you'll run on a treadmill for a bit and if you're a new runner then chances are they'll tell you you overpronate and heel strike (because almost everyone does). They'll then tell you that you need to spend £150+ on supportive shoes to "correct" this.
This is patently nonsense because sticking more cushioning on your feet is not going to correct the issues, which are usually being caused by weak glutes, poor form, and just running slowly (it's almost impossible to run slowly with good form). Instead you're putting the equivalent of a mattress on the bottom of your feet which is not going to help your form improve - if anything it'll make it worse as you've got more weight on your feet.
Good form comes with time, experience and speed. When I was a 60-min 10k runner I was a terrible overpronator. Now at 40 min 10ks I still overpronate a bit, but nothing like to the same extent, mainly because I'm moving quicker and I'm also stronger in the legs and glutes so I'm not just sinking into my feet. If someone in a running shop tells you that buying built-up shoes will help "correct" your gait then you need to run in another direction!
There are great bargains to be had out there OP, it just takes a bit of trial and error to see what suits you.