I’m considering running, which is completely new to me. Any tip on what the wear, how to keep my phone/iPod from falling out of my pocket, how far I should try for, etc…?

basically wear comfortable outfit and but your phone in your back pocket believe me walking or running for a long distance with your phone in your front pocket will not be that great experience , only the pain is enough. for the distance you should try a 2.5 kilometers it's nice distance not too short or too long it's just in sweet spot.
have a nice walk in a lovely day.
peace✌️.

Begin small. Really small, and not fast! Invest into a waist bag for running to keep your phone, keys, and alike, it’s worth it. And remember that 5 minutes run is still better than 0 minutes run.

i used to run before i became chronically ill, and my advice would be: wear something comfortable, cool, and long pants so your legs are kept a bit warm. start with something youre comfortable with, ie. a slower pace, just around the neighbourhood. if you feel like doing another round once youre done, go for it. running will suck for the first week but you have to keep pushing because it becomes the most rewarding thing.

I suggest getting some of those deep pocket leggings or sweatpants cuz that's what I have and put your iPhone or iPod in it and it shouldn't fall out but if it does put it in your like your waistband and if it's new to you probably run about a block or so or even half a block whatever feels comfortable with you and each day out on a little bit more and before you know it you'll be walking a mile