The most important thing about running apparel is that it must be comfortable. It doesn't matter how much does it cost,it just have to be comfortable. You have to feel it. Try your apparel and see if you feel good. It is very wrong to run with uncomfortable apparel, because you won't feel any satisfaction when running. If you feel bad when running, change it the same day, do not try to run one more time with uncomfortable apparel.
In the very beginning I don't suggest you to buy new sport clothes. I believe that you can find some old sport clothes in your wardrobe. If don't just put on a sweater and trousers. Of course, it's good just in the beginning, to try running.
It's not necessary to buy sport trousers in a specialized shop, but you should notice few details:
1. Trousers should be peg-top.
2. It's good if they are tight.
3. It should be very light.
4. It's very comfortable if there is a little pocket inside to keep your keys.
In the summer you should wear simple t-shirts, there's nothing special about them, it just shouldn't be too wide or too little, just pick your size t-shirts and that will be ok.
If you are running then it's a little bit chilly or even cold, you should wear a sweater. There's another topic about running in cold weather and winter. Click here.
It's the best to have cotton or woollen socks, because it sop up sweater very good. Just don't wear to big socks, because it can be uncomfortable to your feet.
It's very good to have short which are made from cotton with nylon and not just from syntetic. Before buying them, try to look if it's comfortable and you can move with no problems. Pull your leg until it's parallel with floor and see if it's ok for you.
Some women doesn't know if it's better to run with bra or not. So just try to run a little bit in your room without it and with it and you will see whitch variant is better for you. A lot of women says that simple bras is not comfortable during running, so the best choice would be to get sport bra.
You need this to watch how much time do you run and to count your pulse. In the beginning you don't have to run some amount of km, you have to run some time (for example 20 minutes), so it's the best to have a watch with chronometer. Believe me, later it will be very pleasant to see that you ran faster to some point or all your route. In the beginning of your running training you should look how much time do you run to one point and try to do the same after one month, you will be very glad to see that you did it faster :)