Huge selection of running shoes now, too many to offer any suggestions.
When I resuming jogging last autumn, after a 40 year hiatus (I'm 63 now, mostly cyclist, just wanted a change up in my workouts), I just grabbed my adidas Daily 2.0 sneakers and started slowly, 100 yards jogging, 100 yards walking, etc., for about a mile out of my usual 5 mile walking loop. They weren't bad for smooth pavement, not great for trail, chipseal or shoulders littered with gravel and debris.
In late November I grabbed a pair of 2019 adidas EQT Gazelles, mostly because adidas run a little narrow and my feet are A or B width, so even the adidas regular width fit okay. And the shoes were only $22 on sale.
I wasn't expecting much but the EQT Gazelles turned out to be appropriate for casual trail running, gravel, rough pavement, chipseal, etc. There's a mid-sole rock plate that doubles as really good arch support -- critical for me because I've always had problems with arch spasms.
I'm up to jogging 3-4 miles out of my usual 5 mile loop, walking half a mile to warm up and cool down. Nothing fast, my fastest splits are around 12'/mile. I can speed-walk nearly that fast, usually 13'-14'/mile. But because it's been so long since I last did any running I'm starting cautiously to avoid injury. My route includes some hills, around 5% grade, on a mix of rough mowed prairie and gravel, some gravel shoulders, some chipseal pavement -- depends on what's available, traffic and road construction issues.
The EQT Gazelles chunky and odd looking, and seemed mostly targeted at the fashion market, although it's built like a proper casual running shoe.
However now I'm looking for something a little lighter and for mostly smooth pavement. The choices are overwhelming. And I haven't found any useful videos on YouTube. I've watched a dozen or so channels and every reviewer is either strictly a fashionista, zero interest in running, or a running channel that's just promoting uncritical spam for sponsors without any evidence of practical road testing.
Ditto most reviews on Amazon, manufacturers and vendors of running shoes. Very little useful content or reviews from runners. Mostly comments about the cosmetics or how comfortable the shoes are for grocery shopping.
So now I'm sifting through a few running oriented websites with actual reviews. But, again, with literally hundreds of choices it's a daunting task.