One of the ladies in our running club swears by ASICS and she ran in the commonwealth games...My brother does marathons, swears by Brooks - my Dad used to do the same and swore by Asics
I'm a consumerist sweatshop supporting whore so I've only ever had Adidas and Nike running shoes, but loved both tbf
I think unless you buy the Nike carbon fibre stuff it make little difference. After that it's about working out if you need a neutral or support shoe. Then it's about what you want in terms of feel (most new runners will want Cushioned shoes).
One thing I will absolutely swear by is you absolutely need to spend the money regardless of your actual ability.