The first 'should' is a downtoner. The speaker doesn't want to say (although he may well have the urge): "Now listen here, you lazy bunch!"
A speaker often begins a speech with "Today, I should (would) like to talk about ..." rather than "Today, I am going to talk about." He wants to invite the audience to join him, rather than order them to listen to his undeniably interesting speech. "Today, I am going to talk about" is addressed to a captive, and perhaps unwilling, audience, for example in a prison or school.
"I should think this is an F-grade paper."
"This is an F." (you worthless waste of space)
Student or Learner