If you are running more than twice a week you will need more than one pair of running shoes. As sports go running is cheap so don't skip on the footwear. I always have a minimum of 8 pairs of running shoes. Sounds extravagant but it isn't. 4 pairs for road & 4 pairs for trail.
Now here is the big tip. For each pair of shoes record how many miles you run. If you buy a decent pair then race up to 150 miles in each pair, train up to 400 miles & plod up to 500 miles. Thereafter use the shoe as for casual purposes & the garden. That way you will reduce the risk of injury to your feet greatly.
Although the evidence for expensive running shoes with regard for injury prevention is fairly minimal, this isn't a bad way to go (if you're organised enough!). It's also good to find 'your' shoes and then buy as many as will fit in the house - bloody shoe companies "improve" them on a regular basis and they're never as good...
Is the n+1 formula used by runners as well as cyclists? As a triathlete I calss myself as neither...