You're going to have to pay more like 2000 to 2500 PLN for a two room apartment, including rent, administration fees and all utilities except telephone/TV/internet. Beware of cheaper apartments, because it usually means there is something majorly wrong with them. They could be inconvenient in terms of transportation. Or they could have, for example, a small kitchen that is impractical to use, so you end up spending more because you eat out rather than cook at home. Or they could have bad windows, which can cost you a lot to heat. Or you could end up having really bad neighbors. Or there might not be any good grocery stores in the area. You get the idea.
My advice is to enlist an OLDER experienced native Polish colleague to help you find the apartment and negotiate with the owner. It will save you a lot of time, money and heartache in the long run. Older experienced Poles know what to look for, and what to avoid. There is no way that you could possibly have a clue.
Location is important, as you don't want to have to commute three hours a day just to save a couple hundred PLN. Getting to work without having to change trams is a great plus, especially in the winter. Do all you can to live near a tram stop on a line that serves your place of work.
I lived in three apartments during my twelve year stay in Poland, and I am very happy that I had older experienced Poles help me. Even though I speak Polish, I would not have done as well as they did. Pay them generously if you must. It's worth every penny.