The beauty of running is that there is not a whole lot of equipment involved. At the most basic level, just a pair of shoes is required. For this reason, you will want to put a lot of attention into this piece of equipment. Sure you need a watch too, but just about any old watch will do (unless you like to track your workouts- then you'll want a GPS watch). But you can't just put any old pair of shoes on your feet.
I recommend that you visit a local running store in order to get a pair of shoes that is made for your foot and the way you run. Running in the right pair of shoes is the first step in preventing injuries. I've had good luck with both Marathon Sports in Wellesley and Charles River Running in Norwood. Marathon Sports will give 10% off trainers and 20% off spikes to students. They will get you in a shoe that works for your running style. How many pairs you buy is up to you. It's not necessary to have a whole stable of shoes like Coach Harte does. I don't recommend it, but some people will run in one pair of shoes all season- one pair for roads, trails, races. I prefer separate road shoes and trail shoes. Some runners will have a pair for practice (trainers) and a pair for races (spikes). What you choose is up to you, but I recommend getting a separate pair of shoes for the trail. Generally, the soles of trail shoes are wide and close to the ground to provide support on uneven surfaces. This will help to prevent your ankle from twisting when you come down on the inevitable bumps or rocks in the woods. Most trail shoes also have protections like a toe bumper and a thicker area between the midsole and outsole to defend against bruising when you step on a stick, rock or root.