My idea would be 600 PLN per month.
You're not going to find an apartment for that little money. The cheapest studio apartment will cost you about 1000 PLN all inclusive (rent, fees and utilities), and I wouldn't count on finding one even that cheap unless you are lucky and have help from an experienced local.
Here's the link your looking for:
You will need the help of a Polish speaker to find an apartment. You won't manage on your own.
Also, when you see the price of an apartment advertised in Poland, that is not the full price, but only the money that the owner receives. For most apartments, there is also a 300 to 600 PLN property maintenance fee, and utilities cost an additional 200 to 600 PLN, depending on the type of heat.
So if you see an apartment advertised for, say, 800 PLN, that means that the total all-inclusive price will be anywhere from 1300 PLN on up. Beware of leaky windows. They can cost you a fortune for heating. Always visit the apartment with an experience (older) local native, and take their advice.