The best shoe to run in is a shoe that matches your gait, running goals and where you are in your running journey. For example, if you a new runner and your goal is run a 5k, a carbon plated shoe might be a little overkill.
Shoes are usually divided into stability and neutral gait shoes. If you tend to over pronate (meaning your ankles tend to rotate outwards) a stability shoe might be more appropriate for your needs. Otherwise if you tend to supinate (ankles rotate in while you run), a neutral gait could be better for you. Short of going to a running shoe store that knows what to look for in gait, a quick look at a well worn pair of your shoes and if the wear is on the side of your big toe (midline), then you might over pronate, and if it is towards your pinky toe, then you might be neutral or supinate while your run.
If your running goal is to start running, a 5k or 10k, we recommend using a more cushioned shoe. Not to endorse specific brands but you’d be looking at Nike Vomero, Saucony Triumph, Adidas Hyperlite and shoes at that level as they will be easier on your joints and make for good training shoes. Of course, this can all be taken with a grain of salt as if your needs are not a one size fits all and another shoe might feel better for you.
Carbon or plated shoes are better for half marathon distances on up or if you are trying to go for a fast time for an upcoming event. Even at that, not completely necessary and should not be used for all your training miles — I personally reserve my carbon shoes for up to 2 weeks before race day and medium distance training runs, to allow my body to adjust to running in them.
While you are able to run in any shoe you want or have, having a dedicated running shoe would be ideal. In this instance, you definitely pay for what you get, but don’t assume you need the $350 shoes right off the bat to get started and as of this writing, something in the $80-$150 price range would most likely fit your needs. Picking your favorite brand and colorway is a bonus too.