Asics/mizno/newbalance/saucony there's your top brands.
You're better off going to a running shop with a dedicated fitting centre, they can discover what your running gait is any select a suitable shoe or failing that buy a fairly neutral shoe then by an insole that works best, there are several reasonable orthotic type insoles that can help i use one by specalized and it works great on and off the bike.
I use saucony grid trigon and i love them, plenty of support but not weighty enough to bog you down or the asics ds trainer is a personal favourite, the mizno wave riders get good writeups as well.