You don't need a permit to live and work in Poland in this case.
However, you haveto register your residence and obtain a certificate of registration of residence (if you plan to stay in Poland longer than 3 months).
Without a residence permit and a PESEL you will get nowhere in Poland. You won't get a Karta Pobytu and that also will cause problems, because otherwise you have to carry your passport with you everywhere.
Working permits for EU citizens are not necessary.
You also will need a NIP (Tax Identication Number). This you get from the local tax office, but once again, you will need to get a PESEL before that.