Acceptable documents for Polish citizens
The primary documents which are used for proving identities are the identity card ("Dowód osobisty") and the passport. Since every Polish is obliged to own an identity card from the age of 18 on you should insist that presented documents is an id card or a passport.
A driver's license usually also is accepted but they do not have an expiry date and so you may be presented a very old (and easily forged) license. That's why I'd consider it a secondary document.
A birth certificate does not contain verifiable personal attributes, but since they are only handed out to the person in question I'd accept them as a secondary document.
Other secondary documents could be company badges, account cards of public transport authorities and the like. You should only accept those if they contain a photo of the person, you have seen those before and you have reason to assume that they are not easily forged.
Note on birth names in Poland
It has been possible for a man to adopt the woman's name at marriage, so both sexes can have a birth name on the id card.
The Polish id card has a size of 86 x 54 mm, is of gray colour with a more reddish stripe on the left side. It is multilayer plastic.
The front side contains a monochrome photo, name (possibly including birth name), date of birth, sex ("K" for woman, "M" for man) and the expiry date. There also is a facsimile of the person's signature.
The backside contains the current address, height, color of eyes, the issuing authority, the date of issuing and three lines of "machine readable data" (nationality, card no, birth date and expiry date, name with some checksum digits in an OCR font).
An id card is valid for up to ten years (five for youths, unlimited for older then 65 years) from the date of issue.
Link to detailed description of the Polish id card (Wikipedia as there is no good description on official pages).
Before 2008 there were also older types of "Dowód osobisty" document in use but they are not official documents anymore.
The blue/purplish lines (front&back) light up under UV light.
Above & below the line "Republic of Poland / Identity Card" extra text lights up under UV.
- Above "Rzeczpospolita Polska"
- Below "Republic of Poland"
- Below that, is not a line. Good eyes or magnifying glasses show text. (Can't read it myself, it's in polish)
- Lower right, a hologram
- midle right, relief. Possibly braille?
- upper right, light-angle variable text. (dob+5 digits, year of expiry + "POL")
- just to the left, variable colour ink. Polish eagle.
Currently there are two versions of driver's license in use in Poland. Both are EU style. It consists of a credit card sized reddish plastic card with several holographic images embedded on the front side. To me this one looks like it is at least as forgery proof as a current ID card.
Since 1998 the EU style driver's license is issued in Poland.
Second version is issued since 2004 (when Poland joined EU).
See also the wikipedia article.