I used to wear ASIC for over 10 years. I notice that the quality has gone down a bit: cheaper material, shorter laces and mostly I cannot find a wider size. I switched to Brooks in 2017 and it seems to be OK (wide size).
I also heard a lot of recommendations for Saucony. Let's hear what the running store's staff suggest.
You're also very on point w.r.t weight training! I quit going to 24-hour fitness in 2015 because of commute change. So now I mostly exercise by running outdoor. I need to sign up for gym again to squat.