Sounds like you are off to a great start! Don't be embarrassed about not being able to ride far. Everyone has to start somewhere and it will be SUCH an accomplishment when you reach your first milestone! There are a lot of folks on here who have done just what you are doing, and their stories are inspirational. Yours will be too!
If you are going to ride in the dark, dusk, dawn, fog, or cloudy day you need lights.
You don't need special clothes to ride. It makes some things easier, but they can be pretty pricey so it's better to accumulate that sort of thing gradually.
What type of riding did you have in mind? It sounds like you are setting up to be a commuter, riding your bike on short trips to work or for errands. You'll need a lock, and don't go too cheap on that. You'll want some way to carry things. A backpack is ok at first but you'll end up with a rack and panniers and/or a basket before long.
I strongly recommend saving up for a seat. Even if the seat costs more than the bike! It will do more for your comfort than anything else. I prefer a brooks saddle which is leather and takes a little time to break in, there are many threads on here that discuss saddles and there are lots of recommendations. You may not notice discomfort on short trips, but the first time you take a longer trip you will notice your saddle!
So for now I recommend helmet, lock, and lights. You might even have a little money left over, but you might save it until you decide what is the next most urgent.
Happy riding!
2009 Trek 7.2FX WSD, brooks Champion Flyer S, commuter bike