Ask your printing guys.
There are firms that only accept EPS, even in this day and age, because they use an outdated (and cheap!) workflow, where often somewhere along the lines "CorelDRAW" gets mentioned. There are even 'print-only' firms that only accept JPEGs.
If your guys are like these, run! and find some other printing guys.
You should be counting "PNG" as one of the formats Not Suitable For Print.
The best possible output – mixed vector and bitmaps, fonts embedded, live transparency and all proper inks (including spot colors) – can only be achieved through PDF. But since there are many ways of creating a PDF and many additional options, you should still ask your printing guys.
Specifically ask for:
- A PDF/X standard: not allowed, optional, or required;
- minimum and maximum bitmap resolutions, for color, grayscale, and black-and-white;
- amount of bleed and slug;
- minimum offset of crop marks;
- recommended color profile;
- correct use and designation of spot colors, if applicable to your job;
- transparency use;
- anything else they have experienced problems with in the past (this may include, for example, badly created DaFont fonts that make their machines crash).