Where should I apply for my visa?

Hi. I'm citizen of Poland living in Dublin. I have got a few question: I'm planning to travel aroud the World next year, just because i don"t know when exactly I'll enter to PRC and where I'll stay, is still possible to get one
- when should i apply if i'm planning to pass the border at he beginning of May
- where should i apply for Tibet Travel Permit
Thank you in advance for all the information
With kind regards Beata