The basics:
A good pair of running shoes log miles you run on the shoes and rotate out when mileage hits 350 500 miles. Ideally, you will have two pair of shoes that you rotate, allowing the shoes time to recover between runs. Hint, start the second pair of shoes at about 250 miles on the first pair of shoes and you will always have a pair that is fresh and a pair that is the trusty standby. Also, you will be better able to gage when the older pair should be retired.
Shorts you have them. Note that shorts made of sport, moisture wicking fibers are better than cotton for most folks. Cotton holds moistures, gets heavy and the fibers can become abrasive. You can find shorts with a built in brief. You have the option of wearing compression shorts (used to be known as bike shorts but without the pad). These are great in preventing chub-rub oin the inner thigh area. Finally as a female you have the option of running skirts.
Tops Sport bra with a moisture wicking top. Again, for most runners cotton is not a friend.
Now for tuning your wear.
As temperatures get cooler you will need to add clothing. The general rule of thumb is to dress as though its 20F warmer than it really is. In other words, as you stand outdoors pre-run you really want to feel cool if not almost cold. Also, think layers. You can peal layer off easily as you or conditions warm.
Below is what I aim for (some taken from Runners World and other sources over time)
60 up Shorts and a shirt either a tank top (singlet) or short sleeved shirt
45 60 short sleeved shirt and shorts
30-45 Long sleeved tech shirt and shorts
30 degrees: 2 tops, 1 bottom. Long-sleeve base layer and a vest keep your core warm. Tights (or shorts, for polar bears).
10 to 20 degrees: 2 tops, 2 bottoms. A jacket over your base layer, and wind pants over the tights.
0 to 10 degrees: 3 tops, 2 bottoms. Two tops (fleece for the cold-prone) and a jacket. Minus 10 to 0 degrees: 3 tops, 2 bottoms, extra pair of mittens, 1 scarf wrapped around mouth or a balaclava.
Minus 20 degrees: 3 tops, 3 bottoms, 2 extra pairs of mittens, 1 balaclava, sunglasses. Or, "Stay inside."
Note that running tights can be found in running stores. They will generally have zippers at the bottom of the legs to allow them to be pulled on or off over shoes. They are form fitting and you can wear shorts over them for modesty, if desired.
A running jacket is usually little more than a wind breaker with added vents. You need a warm to vent off moist air yet be able to zip those paths closed when you turn into a wind.
A great long sleeved running shirt will have a quarter zip on the front to allow heat to escape when temps start to rise.
Hope this helps.