I was thinking 300€ = 1200zly more or less per month with shared expenses to be the minimum for living.
Not enough. Lodz is cheap, but still.
You can rent a room (shared even) but will still cost you around 300ZL.
So now you are down to 900ZL for living the rest of the month + a phone bill probably + transportation etc.
Consider going there with a budget of 2000ZL pr. month, and if you spent less, great.
You might also want to travel around Poland a little, and with a budget of 1200ZL pr. month, that will be very tough..