Działalności gospodarczej sounds good however, what are my obligations to the state, tax wise?
You need to pay 19% income tax plus ZUS. For the first two years ZUS is 250zl per month (flat fee) and after that it is 850zl per month.
where should I go and submit?
According to poznan.uw.gov.pl/c/portal/layout?p_l_id=PUB.1016.11 it's the Department of Citizens and Foreigners Affairs at pl. Wolności 17, 61-739 Poznań
(tel.: +48 61 854 19 17, 61 854 17 74, 61 854 13 97
fax: +48 61 854 18 43)
that handles among others; issues pertaining to passports, foreigners, citizenship and repatriation.
You probably won't need a lawyer, just somebody who speaks Polish.