Getting Letter of Marque depended on the political climate at the time. If it was a time of relative peace, then it is difficult to get a letter because the monarch is going to try and keep the relations with the other countries peaceful. If there was hostility, like in the case of Britain and Spain, then it was fairly easy to attain one. But it should be noted that the letters of marque were supposed to be a way for an individual to compensate themselves for a piratical action they had experienced at the hands of said country. And before the letter was issued, they had to try and gain compensation through diplomatic channels, and then if that failed, the letter was issued.

So it varied on how difficult it was to get a letter of marque.

As for reading, I recommend Google. There are lots of good articles out there on privateering. Even better is JSTOR, which is an online library that has academic articles available for reading. The one downside with JSTOR is that you need a membership or to be attending an academic institution.