When i took up running, in a pair of cheap, but proper, neutral running shoes, i was always having ITB issues on my dodgy leg. I had my gait analysed and I over pronate a lot, so tried some stability ones (mizumo wave inspire’s … Not that pricey, £60 iirc). Massive improvement. Always used stability shoes since.
Possible massive coincidence, and a sample size of 1 and all that, but it worked for me.
My only tip is to try them on and run for a while on the treadmill, as I’ve often found that the ones that suit me aren’t necessarily the most pricey.