Looking for affordable accommodation in warsaw

My mother and I are on a very special journey together as we are both going to pursue are degrees together at Vistula University. We're looking for an accommodation for our stay in warsaw and would love to move in on the 1st of November. We will be living here with my 10-year-old sister ?. We're looking for an apartment or even a room with a king-sized bed for us to stay together. It has to be close to public transportation. My mother and I are both clean and neat people. We do not mind extroverted or introverted people. Our budget for the accommodation with all bills, extra is 3100 zl. I hope I can find an amazing place to stay for my family.