One of the most common reasons that runners struggle to find their perfect running shoe has less to do with the shoe itself, usually, and more the fact that they are not getting a shoe that correctly fits their foot. There is a fine line between having a shoe that has too much room or not enough room, and one that is just right. Aim to find a shoe in a half size larger than what you typically wear in other styles of shoe. This will ensure that you have just enough wiggle room for your toes, to accommodate for any swelling or shrinking of the feet that might happen (it happens! toes and fingers tend to shrink during the cold, dryer months and puff up and swell due to water retention and warmer temperatures in the summer) as well as to give you some "give" as you increase and decrease your pace. Aim for about a thumb's width of room between the end of your big toe and the inside toe of the shoe, as a rule of thumb for measuring (pun intended).
You also want to be sure you find a pair of shoes that closely and comfortably envelop your foot without being too constricting. You want a shoe that is secure and firm, to avoid chafing and too much movement of the foot within the shoe, as well to help keep the foot secure to help avoid prevent future injuries. (If you have a chronic or already existing injury or foot problem like weak arches or plantar fasciitis, it is even more important to find the right fitting shoe. You will want to look for ones with plenty of arch support and cushioning, and ones that have enough support around the ankle to keep the ankles steady and prevent pronation.) The same principle applies to how the shoe fits at the heel of the foot. You certainly do not want too loose of a heel so that you annoyingly raise up in and out of the shoe as you run. Loose heels also mean a greater risk of painful blisters.
Be sure to tie your shoes correctly as well. You will want them tied loose enough so that they don't constrict your feet and cause aching, but tight enough to hold the shoe securely to your foot.