Taking a multi-tool like a Swiss Army knife (doesn't have to be this, but just for reference) is a pretty important staple in hiking outdoor gear. If you're not planning on a long trip or camping, it's still important as a "you never know" kind of tool. You can even pick them up cheap now.
A great, comfortable pair of water-proof hiking boots are also key. The boots help to stabilize your feet and ankles during uneven terrain. Having a pair that is water-proof is good because you never know if/when you'll encounter unexpected water and you want to remain dry.
This is one of the most essential pieces of outdoor gear you can take with you for hiking. It's the thing you will store all of the other needed supplies in. You don't want anything too bulky that it'll weigh you down, so be wary of that. Try on a few before you buy. Make sure it has the right amount of space and/or pockets for you to put all of your essential hiking supplies in it, too.